Learning financial theories and strategies requires an understanding of mathematical symbols. These symbols are used as shorthand to explain theoretical ideas in economics textbooks, theories, and analysis papers.

As such, economists have to have some quantitative expertise. The extra snug they’re with math and econometrics, the higher for his or her analysis and profession alternatives.

However, economists should not mathematicians. So, when college students of economics take Bachelor’s or Grasp’s courses whereas learning for his or her economics degree, they is likely to be offered with symbol-heavy lecture notes. With out understanding these symbols, college students will most likely battle to learn them, leaving their which means unclear.

This text goals to fill that hole. What are probably the most generally used math symbols in economics, and what do they imply?

## Symbols and definitions

*Math symbols*

- (pm) – this image means “plus or minus”. It’s most frequently used when describing an interval of some kind, akin to a confidence interval.
- (preceq) – this image, and others prefer it, are used typically in economics to explain choice relations. Preferences are the constructing blocks of the demand curve. This image is seldom used outdoors of microeconomics programs that particularly deal with preferences.
- (propto) – this image signifies that the variable on the left aspect is proportional to the variable on the proper aspect.
- (sim) – this image means “just like”.
- (approx) – this image means “roughly”, which implies one thing is nearly, however not fairly, equal to one thing else.
- (parallel) – parallel. In economics, that is used most frequently in econometrics when describing how issues relate to one another geometrically.
- (perp) – this implies perpendicular or “orthogonal”. Perpendicular means two issues intersect at a 90 diploma angle in geometry. In econometrics, orthogonal signifies that one variable has zero energy to elucidate one other variable, as a result of they’ve a covariance equal to zero.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (otimes) – this image is used to explain the Kronecker product, which is a matrix algebra idea that comes up often in econometrics.
- (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.- (cdot) this image is positioned above a variable to indicate the by-product with respect to time of that variable. This image is usually utilized in macroeconomics, however seldom outdoors of that context.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (alpha) – the letter alpha, typically used with Cobb-Douglas capabilities to indicate the exponents. Additionally used when discussing p-values in speculation testing; the “alpha” degree units the quantity that you simply evaluate the speculation take a look at’s consequence to, as a way to decide if the result’s statistically vital (akin to 0.05 for five% significance, which is commonly the default).
- (beta) – the letter beta, additionally used as an exponent in Cobb-Douglas capabilities. However, it’s most famously used when describing regression formulae. In that context, this letter normally has a subscript and is the shorthand means of claiming “the regression coefficient on the variable it’s being multiplied with”.
- (epsilon) – the letter epsilon. This letter can also be generally utilized in regression evaluation, and normally denotes the error time period of the regression. Many introductory econometrics lessons, and every other course that showcases regression evaluation, will make frequent use of this image. Most of the assumptions that permit economists to justify utilizing a regression mannequin contain statements made in regards to the error time period.
- (delta) – the letter delta. This image is used typically to indicate the change in a variable, or depreciation in macroeconomics. It’s typically confused with the image for partial derivatives, which seems very comparable!
- (lambda) – the letter lambda. It’s used most frequently when fixing constrained optimization issues utilizing the Lagrangian method; on this case it stands for the shadow worth of the funds constraint. This letter shall be seen fairly often by microeconomics college students.
- (mu) – the letter mu. This letter is used typically in statistics and normally denotes the imply, or common, of one thing.
- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (sigma) – the decrease case sigma. Used typically in regression evaluation and statistics to indicate normal deviation; when squared, it’s the variance of the topic in query.
- (Phi) – the capital letter phi. Often used to indicate a chance distribution in statistics, mostly the cumulative distribution perform (cdf) of the conventional distribution.
- (phi) – the decrease case phi. Usually used to indicate the chance distribution perform (pdf) of the conventional distribution in statistics. However, this letter is ceaselessly used outdoors of this context too, not like the capital model described above.
- (chi) – the letter chi. Utilized in statistics to indicate the chi-squared distribution, which is a chance distribution that’s used so much in regression evaluation.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

The next letters normally don’t carry particular which means on their very own, however are sometimes utilized in economics regardless. They’re generally used as placeholders for a variable when discussing a concept or equation.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing. - (overline{X}): the bar above a variable denotes the typical. This image is used fairly often in financial formulae, for instance when describing the sum of least squares.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (subset) – this image exhibits that the variable or group on the left aspect of it’s a subset of (included in) the group on the proper aspect of it. With a slash by it, it means the alternative.
- (subseteq) – the identical because the above image, besides that the subset it describes will also be equal to the variable or group on the proper aspect. It doesn’t need to be utterly contained inside the second group.
- (supset) – this image denotes a superset, which is the alternative of a subset. It signifies that the group on the left aspect of this image comprises the group on the proper aspect.
- (cap) – that is the image for the intersection of two units, or the issues they each include which can be the identical.
- (cup) – that is the image for the union of two units, or every little thing that’s contained in at the least one of many units.
- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists) means “there exists at the least one”. It’s generally seen in proofs, which are typically utilized in econometrics- or statistics-heavy programs.
- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (forall) means “for all”, normally within the context of stating some reality in an econometric context, i.e., stating {that a} explicit equation is true for all i in some set of noticed values N.
- (implies) means “implies”; the perform, components, or variable on the left aspect implies some relationship written on the proper aspect.
- (iff) means “if and provided that”.

## Studying financial formulae

Now that the generally used symbols have been launched, we will use them to learn and interpret an financial components. The beneath instance is the Goldsmith equation, utilized in macroeconomics to explain the expansion of capital inventory over time:

start{equation*}

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

The primary variable on this components stands for the by-product of capital with respect to time, signified by the dot above the *Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

That is equal to the funding (which right here is outlined as *I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

Then, on the far right-hand aspect, It’s damaged down additional. It’s multiplied by *s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}start{equation*}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

This equation, in the meantime, describes the income elasticity of demand with respect to good A. It tells us precisely what this elasticity is and learn how to calculate it. The earnings elasticity of demand *YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

This components is a foundational theorem in econometrics, often known as the Regulation of Iterated Expectations. Recall that the (mathbb{E}) image means “expectation”. This components states the next in mathematical shorthand.

Our expectation of *X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

In additional exact statistical language, this components signifies that the anticipated worth of *X* is the same as the expectation of the conditional expectation of *X* given *Y*.

It took many phrases to explain what a easy components may convey with only some symbols. Clearly, utilizing these symbols may also help economists talk concepts rather more successfully than by simply utilizing phrases!

Learning financial theories and strategies requires an understanding of mathematical symbols. These symbols are used as shorthand to explain theoretical ideas in economics textbooks, theories, and analysis papers.

As such, economists have to have some quantitative expertise. The extra snug they’re with math and econometrics, the higher for his or her analysis and profession alternatives.

However, economists should not mathematicians. So, when college students of economics take Bachelor’s or Grasp’s courses whereas learning for his or her economics degree, they is likely to be offered with symbol-heavy lecture notes. With out understanding these symbols, college students will most likely battle to learn them, leaving their which means unclear.

This text goals to fill that hole. What are probably the most generally used math symbols in economics, and what do they imply?

## Symbols and definitions

*Math symbols*

- (pm) – this image means “plus or minus”. It’s most frequently used when describing an interval of some kind, akin to a confidence interval.
- (preceq) – this image, and others prefer it, are used typically in economics to explain choice relations. Preferences are the constructing blocks of the demand curve. This image is seldom used outdoors of microeconomics programs that particularly deal with preferences.
- (propto) – this image signifies that the variable on the left aspect is proportional to the variable on the proper aspect.
- (sim) – this image means “just like”.
- (approx) – this image means “roughly”, which implies one thing is nearly, however not fairly, equal to one thing else.
- (parallel) – parallel. In economics, that is used most frequently in econometrics when describing how issues relate to one another geometrically.
- (perp) – this implies perpendicular or “orthogonal”. Perpendicular means two issues intersect at a 90 diploma angle in geometry. In econometrics, orthogonal signifies that one variable has zero energy to elucidate one other variable, as a result of they’ve a covariance equal to zero.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (otimes) – this image is used to explain the Kronecker product, which is a matrix algebra idea that comes up often in econometrics.
- (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.- (cdot) this image is positioned above a variable to indicate the by-product with respect to time of that variable. This image is usually utilized in macroeconomics, however seldom outdoors of that context.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (alpha) – the letter alpha, typically used with Cobb-Douglas capabilities to indicate the exponents. Additionally used when discussing p-values in speculation testing; the “alpha” degree units the quantity that you simply evaluate the speculation take a look at’s consequence to, as a way to decide if the result’s statistically vital (akin to 0.05 for five% significance, which is commonly the default).
- (beta) – the letter beta, additionally used as an exponent in Cobb-Douglas capabilities. However, it’s most famously used when describing regression formulae. In that context, this letter normally has a subscript and is the shorthand means of claiming “the regression coefficient on the variable it’s being multiplied with”.
- (epsilon) – the letter epsilon. This letter can also be generally utilized in regression evaluation, and normally denotes the error time period of the regression. Many introductory econometrics lessons, and every other course that showcases regression evaluation, will make frequent use of this image. Most of the assumptions that permit economists to justify utilizing a regression mannequin contain statements made in regards to the error time period.
- (delta) – the letter delta. This image is used typically to indicate the change in a variable, or depreciation in macroeconomics. It’s typically confused with the image for partial derivatives, which seems very comparable!
- (lambda) – the letter lambda. It’s used most frequently when fixing constrained optimization issues utilizing the Lagrangian method; on this case it stands for the shadow worth of the funds constraint. This letter shall be seen fairly often by microeconomics college students.
- (mu) – the letter mu. This letter is used typically in statistics and normally denotes the imply, or common, of one thing.
- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (sigma) – the decrease case sigma. Used typically in regression evaluation and statistics to indicate normal deviation; when squared, it’s the variance of the topic in query.
- (Phi) – the capital letter phi. Often used to indicate a chance distribution in statistics, mostly the cumulative distribution perform (cdf) of the conventional distribution.
- (phi) – the decrease case phi. Usually used to indicate the chance distribution perform (pdf) of the conventional distribution in statistics. However, this letter is ceaselessly used outdoors of this context too, not like the capital model described above.
- (chi) – the letter chi. Utilized in statistics to indicate the chi-squared distribution, which is a chance distribution that’s used so much in regression evaluation.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

The next letters normally don’t carry particular which means on their very own, however are sometimes utilized in economics regardless. They’re generally used as placeholders for a variable when discussing a concept or equation.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing. - (overline{X}): the bar above a variable denotes the typical. This image is used fairly often in financial formulae, for instance when describing the sum of least squares.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (subset) – this image exhibits that the variable or group on the left aspect of it’s a subset of (included in) the group on the proper aspect of it. With a slash by it, it means the alternative.
- (subseteq) – the identical because the above image, besides that the subset it describes will also be equal to the variable or group on the proper aspect. It doesn’t need to be utterly contained inside the second group.
- (supset) – this image denotes a superset, which is the alternative of a subset. It signifies that the group on the left aspect of this image comprises the group on the proper aspect.
- (cap) – that is the image for the intersection of two units, or the issues they each include which can be the identical.
- (cup) – that is the image for the union of two units, or every little thing that’s contained in at the least one of many units.
- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists) means “there exists at the least one”. It’s generally seen in proofs, which are typically utilized in econometrics- or statistics-heavy programs.
- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (forall) means “for all”, normally within the context of stating some reality in an econometric context, i.e., stating {that a} explicit equation is true for all i in some set of noticed values N.
- (implies) means “implies”; the perform, components, or variable on the left aspect implies some relationship written on the proper aspect.
- (iff) means “if and provided that”.

## Studying financial formulae

Now that the generally used symbols have been launched, we will use them to learn and interpret an financial components. The beneath instance is the Goldsmith equation, utilized in macroeconomics to explain the expansion of capital inventory over time:

start{equation*}

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

The primary variable on this components stands for the by-product of capital with respect to time, signified by the dot above the *Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

That is equal to the funding (which right here is outlined as *I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

Then, on the far right-hand aspect, It’s damaged down additional. It’s multiplied by *s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}start{equation*}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

This equation, in the meantime, describes the income elasticity of demand with respect to good A. It tells us precisely what this elasticity is and learn how to calculate it. The earnings elasticity of demand *YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

This components is a foundational theorem in econometrics, often known as the Regulation of Iterated Expectations. Recall that the (mathbb{E}) image means “expectation”. This components states the next in mathematical shorthand.

Our expectation of *X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

In additional exact statistical language, this components signifies that the anticipated worth of *X* is the same as the expectation of the conditional expectation of *X* given *Y*.

It took many phrases to explain what a easy components may convey with only some symbols. Clearly, utilizing these symbols may also help economists talk concepts rather more successfully than by simply utilizing phrases!

Learning financial theories and strategies requires an understanding of mathematical symbols. These symbols are used as shorthand to explain theoretical ideas in economics textbooks, theories, and analysis papers.

As such, economists have to have some quantitative expertise. The extra snug they’re with math and econometrics, the higher for his or her analysis and profession alternatives.

However, economists should not mathematicians. So, when college students of economics take Bachelor’s or Grasp’s courses whereas learning for his or her economics degree, they is likely to be offered with symbol-heavy lecture notes. With out understanding these symbols, college students will most likely battle to learn them, leaving their which means unclear.

This text goals to fill that hole. What are probably the most generally used math symbols in economics, and what do they imply?

## Symbols and definitions

*Math symbols*

- (pm) – this image means “plus or minus”. It’s most frequently used when describing an interval of some kind, akin to a confidence interval.
- (preceq) – this image, and others prefer it, are used typically in economics to explain choice relations. Preferences are the constructing blocks of the demand curve. This image is seldom used outdoors of microeconomics programs that particularly deal with preferences.
- (propto) – this image signifies that the variable on the left aspect is proportional to the variable on the proper aspect.
- (sim) – this image means “just like”.
- (approx) – this image means “roughly”, which implies one thing is nearly, however not fairly, equal to one thing else.
- (parallel) – parallel. In economics, that is used most frequently in econometrics when describing how issues relate to one another geometrically.
- (perp) – this implies perpendicular or “orthogonal”. Perpendicular means two issues intersect at a 90 diploma angle in geometry. In econometrics, orthogonal signifies that one variable has zero energy to elucidate one other variable, as a result of they’ve a covariance equal to zero.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (otimes) – this image is used to explain the Kronecker product, which is a matrix algebra idea that comes up often in econometrics.
- (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.- (cdot) this image is positioned above a variable to indicate the by-product with respect to time of that variable. This image is usually utilized in macroeconomics, however seldom outdoors of that context.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (alpha) – the letter alpha, typically used with Cobb-Douglas capabilities to indicate the exponents. Additionally used when discussing p-values in speculation testing; the “alpha” degree units the quantity that you simply evaluate the speculation take a look at’s consequence to, as a way to decide if the result’s statistically vital (akin to 0.05 for five% significance, which is commonly the default).
- (beta) – the letter beta, additionally used as an exponent in Cobb-Douglas capabilities. However, it’s most famously used when describing regression formulae. In that context, this letter normally has a subscript and is the shorthand means of claiming “the regression coefficient on the variable it’s being multiplied with”.
- (epsilon) – the letter epsilon. This letter can also be generally utilized in regression evaluation, and normally denotes the error time period of the regression. Many introductory econometrics lessons, and every other course that showcases regression evaluation, will make frequent use of this image. Most of the assumptions that permit economists to justify utilizing a regression mannequin contain statements made in regards to the error time period.
- (delta) – the letter delta. This image is used typically to indicate the change in a variable, or depreciation in macroeconomics. It’s typically confused with the image for partial derivatives, which seems very comparable!
- (lambda) – the letter lambda. It’s used most frequently when fixing constrained optimization issues utilizing the Lagrangian method; on this case it stands for the shadow worth of the funds constraint. This letter shall be seen fairly often by microeconomics college students.
- (mu) – the letter mu. This letter is used typically in statistics and normally denotes the imply, or common, of one thing.
- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (sigma) – the decrease case sigma. Used typically in regression evaluation and statistics to indicate normal deviation; when squared, it’s the variance of the topic in query.
- (Phi) – the capital letter phi. Often used to indicate a chance distribution in statistics, mostly the cumulative distribution perform (cdf) of the conventional distribution.
- (phi) – the decrease case phi. Usually used to indicate the chance distribution perform (pdf) of the conventional distribution in statistics. However, this letter is ceaselessly used outdoors of this context too, not like the capital model described above.
- (chi) – the letter chi. Utilized in statistics to indicate the chi-squared distribution, which is a chance distribution that’s used so much in regression evaluation.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

The next letters normally don’t carry particular which means on their very own, however are sometimes utilized in economics regardless. They’re generally used as placeholders for a variable when discussing a concept or equation.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing. - (overline{X}): the bar above a variable denotes the typical. This image is used fairly often in financial formulae, for instance when describing the sum of least squares.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (subset) – this image exhibits that the variable or group on the left aspect of it’s a subset of (included in) the group on the proper aspect of it. With a slash by it, it means the alternative.
- (subseteq) – the identical because the above image, besides that the subset it describes will also be equal to the variable or group on the proper aspect. It doesn’t need to be utterly contained inside the second group.
- (supset) – this image denotes a superset, which is the alternative of a subset. It signifies that the group on the left aspect of this image comprises the group on the proper aspect.
- (cap) – that is the image for the intersection of two units, or the issues they each include which can be the identical.
- (cup) – that is the image for the union of two units, or every little thing that’s contained in at the least one of many units.
- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists) means “there exists at the least one”. It’s generally seen in proofs, which are typically utilized in econometrics- or statistics-heavy programs.
- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (forall) means “for all”, normally within the context of stating some reality in an econometric context, i.e., stating {that a} explicit equation is true for all i in some set of noticed values N.
- (implies) means “implies”; the perform, components, or variable on the left aspect implies some relationship written on the proper aspect.
- (iff) means “if and provided that”.

## Studying financial formulae

Now that the generally used symbols have been launched, we will use them to learn and interpret an financial components. The beneath instance is the Goldsmith equation, utilized in macroeconomics to explain the expansion of capital inventory over time:

start{equation*}

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

The primary variable on this components stands for the by-product of capital with respect to time, signified by the dot above the *Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

That is equal to the funding (which right here is outlined as *I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

Then, on the far right-hand aspect, It’s damaged down additional. It’s multiplied by *s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}start{equation*}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

This equation, in the meantime, describes the income elasticity of demand with respect to good A. It tells us precisely what this elasticity is and learn how to calculate it. The earnings elasticity of demand *YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

This components is a foundational theorem in econometrics, often known as the Regulation of Iterated Expectations. Recall that the (mathbb{E}) image means “expectation”. This components states the next in mathematical shorthand.

Our expectation of *X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

In additional exact statistical language, this components signifies that the anticipated worth of *X* is the same as the expectation of the conditional expectation of *X* given *Y*.

It took many phrases to explain what a easy components may convey with only some symbols. Clearly, utilizing these symbols may also help economists talk concepts rather more successfully than by simply utilizing phrases!

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.

## Symbols and definitions

*Math symbols*

- (sim) – this image means “just like”.
- (in) – this implies “in”, {that a} variable on the left aspect is contained inside a variable, group, or idea on the proper aspect. It may be reversed to imply the alternative. For instance, typically in economics, a concept will describe which values of
*x*are attainable. If*x*can solely tackle actual quantity values, the outline may begin with*x*(in) (mathbb{R}). Which means*x*can solely be an actual quantity, as a result of it’s “in” the set of (mathbb{R}). - (partial) means “partial”, and is used to indicate a partial by-product.
*I*is commonly used to indicate the identification matrix with dimension_{N}*N*; it’s used ceaselessly in statistics and econometrics.

*Greek letters*

These are sometimes used to indicate variables, however some carry particular which means due to how typically they’ve been utilized in sure contexts.

- (rho) – the letter rho. Usually used to point the correlation coefficient between two variables.
- (Sigma) – the capital letter sigma. Used ceaselessly to indicate the sum of issues.
- (Omega) – the capital letter omega. Used typically in econometrics to be the image for a matrix.

- (gamma) – the letter gamma.
- (eta) – the letter eta.
- (kappa) – the letter kappa.
- (nu) – the letter nu.
- (tau) – the letter tau.
- (upsilon) – the letter upsilon.
- (Psi) – the capital letter psi.
- (psi) – the decrease case letter psi.
- (omega) – the decrease case letter omega.

*Different statistics symbols*

The next symbols are sometimes utilized in financial statistics contexts. Word that the Greek letters above include many symbols utilized in these contexts as nicely.

- | means “on condition that” in a statistics sense, i.e.,
*X*|*Y*= 2 means “*X*given the truth that*Y*equals 2”. - (mathbb{E}) means “the expectation of”. Sometimes there’s a outlined variable, matrix, and so on. positioned in brackets subsequent to it (for instance,
*X*); then, this implies the expectation, or anticipated worth, of*X*. This image is used extraordinarily typically in statistics. - (mathbb{V}) means “the variance of”. It’s utilized in the identical means because the expectation image above, so when one thing is positioned in brackets subsequent to this, it means the variance of that variable, matrix, and so on. To not be confused with (sigma)
^{2}, which stands for a selected quantity. - (sigma)
^{2}is the image for the variance of a variable, matrix, and so on. This stands for the precise quantity that’s the variance of one thing.

*Set concept symbols*

Set concept is used to explain how teams of issues relate to 1 one other. They’re just like a Venn diagram, however within the language of math.

- (emptyset) – that is the “empty set” image, which is just a set that comprises nothing.

*Units of numbers*

The next symbols are nonetheless technically units as they describe teams of numbers, like “rational numbers” or “pure numbers”. These are used fairly often in financial formulae even when different set symbols may not seem.

- (mathbb{N}) is the image for pure numbers.
- (mathbb{Z}) is the image for the set together with all integers.
- (mathbb{Q}) is the image for the set of all rational numbers.
- (mathbb{R}) is the image for the set of all actual numbers.

*Different helpful symbols*

- (exists!) is a variation on the image above meaning “there exists one and just one”.
- (iff) means “if and provided that”.

## Studying financial formulae

dot{K_t} = mathit{I_t}-deltamathit{K_t} = mathit{s}F(mathit{K_t},,mathit{A_t},mathit{L_t}) – deltamathit{K_t}

finish{equation*}

*Ok _{t}*. Recall from the checklist of math symbols above that the dot means the derivative of one thing with respect to time.

*I _{t}*) at a cut-off date minus the depreciation instances the capital inventory at a cut-off date. Recall that the image (delta) from above is commonly used to indicate depreciation.

*s*, which stands for the financial savings price. That is multiplied by a perform of capital, labor, and technological progress. The perform’s precise kind isn’t outlined for us but, so it’s merely written as *F*(*Ok _{t}*,

*A*,

_{t}*L*), which is widespread apply in math.

_{t}

mathit{YED}_{A} = frac{Deltamathit{q}_{A}}{Deltamathit{Y}} = frac{frac{partial{q}_{A}}{mathit{q}_{A}}}{frac{partial{Y}}{Y}}

finish{equation*}

*YED _{A}* is the same as the change within the amount demanded divided by the change in earnings.

start{equation*}

mathbb{E}[X] = mathbb{E}[mathbb{E}[X|Y]]

finish{equation*}

*X* typically is the same as our expectation of the worth of *X* that’s anticipated given some worth that the variable *Y* may tackle. In different phrases, we’ve got some normal thought of what *X* ought to be over the entire vary of attainable *Y* values (which haven’t been outlined but). This expectation is identical as what we typically count on *X* to be.

*X* is the same as the expectation of the conditional expectation of *X* given *Y*.