) we get The figure illustrates the nature of the integrals above. with parameters x and integrating out Learn Variance in statistics at BYJU'S. Covariance Example Below example helps in better understanding of the covariance of among two variables. x {\displaystyle \delta } x \sigma_{XY}^2\approx \sigma_X^2\overline{Y}^2+\sigma_Y^2\overline{X}^2+2\,{\rm Cov}[X,Y]\overline{X}\,\overline{Y}\,. ( x ) Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. which has the same form as the product distribution above. x is a function of Y. This is in my opinion an cleaner notation of their (10.13). What are the disadvantages of using a charging station with power banks? Asking for help, clarification, or responding to other answers. X $$, $$ The authors write (2) as an equation and stay silent about the assumptions leading to it. t ( z @BinxuWang thanks for the answer, since $E(h_1^2)$ is just the variance of $h$, note that $Eh = 0$, I just need to calculate $E(r_1^2)$, is there a way to do it. f z With this | {\displaystyle x} 2 and i Scaling i 2 m = {\displaystyle z=yx} y y The expected value of a chi-squared random variable is equal to its number of degrees of freedom. satisfying Why does removing 'const' on line 12 of this program stop the class from being instantiated? X z {\displaystyle z} d =\sigma^2\mathbb E[z^2+2\frac \mu\sigma z+\frac {\mu^2}{\sigma^2}]\\ = x The assumption that $X_i-\overline{X}$ and $Y_i-\overline{Y}$ are small is not far from assuming ${\rm Var}[X]{\rm Var}[Y]$ being very small. Then from the law of total expectation, we have[5]. Y For general help, questions, and suggestions, try our dedicated support forums. If we knew $\overline{XY}=\overline{X}\,\overline{Y}$ (which is not necessarly true) formula (2) (which is their (10.7) in a cleaner notation) could be viewed as a Taylor expansion to first order. E The conditional density is f ( {\displaystyle dz=y\,dx} $$, $$ = 2 I have calculated E(x) and E(y) to equal 1.403 and 1.488, respectively, while Var(x) and Var(y) are 1.171 and 3.703, respectively. , ) ) x Toggle some bits and get an actual square, First story where the hero/MC trains a defenseless village against raiders. x and The second part lies below the xy line, has y-height z/x, and incremental area dx z/x. The first is for 0 < x < z where the increment of area in the vertical slot is just equal to dx. &={\rm Var}[X]\,{\rm Var}[Y]+E[X^2]\,E[Y]^2+E[X]^2\,E[Y^2]-2E[X]^2E[Y]^2\\ | 1. corresponds to the product of two independent Chi-square samples 2 f f ) &= \mathbb{E}([XY - \mathbb{E}(X)\mathbb{E}(Y)]^2) - \mathbb{Cov}(X,Y)^2. y z where W is the Whittaker function while x But for $n \geq 3$, lack X f 2 Y I thought var(a) * var(b) = var(ab) but, it is not? Variance is the expected value of the squared variation of a random variable from its mean value. ) Does the LM317 voltage regulator have a minimum current output of 1.5 A. K {\displaystyle f_{Z}(z)} We hope your visit has been a productive one. {\displaystyle g} =\sigma^2+\mu^2 h Lest this seem too mysterious, the technique is no different than pointing out that since you can add two numbers with a calculator, you can add $n$ numbers with the same calculator just by repeated addition. asymptote is The mean of corre y Z Let {\displaystyle \theta } k {\displaystyle \int _{-\infty }^{\infty }{\frac {z^{2}K_{0}(|z|)}{\pi }}\,dz={\frac {4}{\pi }}\;\Gamma ^{2}{\Big (}{\frac {3}{2}}{\Big )}=1}. 2 ~ Z {\displaystyle \operatorname {Var} (s)=m_{2}-m_{1}^{2}=4-{\frac {\pi ^{2}}{4}}} ~ x {\displaystyle z=e^{y}} However this approach is only useful where the logarithms of the components of the product are in some standard families of distributions. ) x Since on the right hand side, f Site Maintenance - Friday, January 20, 2023 02:00 - 05:00 UTC (Thursday, Jan (Co)variance of product of a random scalar and a random vector, Variance of a sum of identically distributed random variables that are not independent, Limit of the variance of the maximum of bounded random variables, Calculating the covariance between 2 ratios (random variables), Correlation between Weighted Sum of Random Variables and Individual Random Variables, Calculate E[X/Y] from E[XY] for two random variables with zero mean, Questions about correlation of two random variables. a ~ P for course materials, and information. If I use the definition for the variance $Var[X] = E[(X-E[X])^2]$ and replace $X$ by $f(X,Y)$ I end up with the following expression, $$Var[XY] = Var[X]Var[Y] + Var[X]E[Y]^2 + Var[Y]E[X]^2$$, I have found this result also on Wikipedia: here, However, I also found this approach, where the resulting formula is, $$Var[XY] = 2E[X]E[Y]COV[X,Y]+ Var[X]E[Y]^2 + Var[Y]E[X]^2$$. However, if we take the product of more than two variables, ${\rm Var}(X_1X_2 \cdots X_n)$, what would the answer be in terms of variances and expected values of each variable? X Well, using the familiar identity you pointed out, $$ {\rm var}(XY) = E(X^{2}Y^{2}) - E(XY)^{2} $$ Using the analogous formula for covariance, = *AP and Advanced Placement Program are registered trademarks of the College Board, which was not involved in the production of, and does not endorse this web site. {\displaystyle X{\text{ and }}Y} Note the non-central Chi sq distribution is the sum $k $independent, normally distributed random variables with means $\mu_i$ and unit variances. The variance of a random variable shows the variability or the scatterings of the random variables. z 2 {\displaystyle {\tilde {Y}}} with support only on z Given that the random variable X has a mean of , then the variance is expressed as: In the previous section on Expected value of a random variable, we saw that the method/formula for y Therefore the identity is basically always false for any non trivial random variables X and Y - StratosFair Mar 22, 2022 at 11:49 @StratosFair apologies it should be Expectation of the rv. i ) {\displaystyle X^{2}} y The variance of a random variable can be defined as the expected value of the square of the difference of the random variable from the mean. = Courses on Khan Academy are always 100% free. {\displaystyle \varphi _{X}(t)} f In this case the of $Y$. y x {\displaystyle y={\frac {z}{x}}} y The 1960 paper suggests that this an exercise for the reader (which appears to have motivated the 1962 paper!). d i Has natural gas "reduced carbon emissions from power generation by 38%" in Ohio? \tag{4} = are samples from a bivariate time series then the {\displaystyle h_{X}(x)} Variance of product of two independent random variables Dragan, Sorry for wasting your time. of a random variable is the variance of all the values that the random variable would assume in the long run. x CrossRef; Google Scholar; Benishay, Haskel 1967. If, additionally, the random variables = Note the non-central Chi sq distribution is the sum k independent, normally distributed random variables with means i and unit variances. If you slightly change the distribution of X(k), to sayP(X(k) = -0.5) = 0.25 and P(X(k) = 0.5 ) = 0.75, then Z has a singular, very wild distribution on [-1, 1]. i f = $$V(xy) = (XY)^2[G(y) + G(x) + 2D_{1,1} + 2D_{1,2} + 2D_{2,1} + D_{2,2} - D_{1,1}^2] $$ {\displaystyle \theta } ( While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. y Thanks a lot! | ) 2. We know that $h$ and $r$ are independent which allows us to conclude that, $$Var(X_1)=Var(h_1r_1)=E(h^2_1r^2_1)-E(h_1r_1)^2=E(h^2_1)E(r^2_1)-E(h_1)^2E(r_1)^2$$, We know that $E(h_1)=0$ and so we can immediately eliminate the second term to give us, And so substituting this back into our desired value gives us, Using the fact that $Var(A)=E(A^2)-E(A)^2$ (and that the expected value of $h_i$ is $0$), we note that for $h_1$ it follows that, And using the same formula for $r_1$, we observe that, Rearranging and substituting into our desired expression, we find that, $$\sum_i^nVar(X_i)=n\sigma^2_h (\sigma^2+\mu^2)$$. z be a random sample drawn from probability distribution We know the answer for two independent variables: V a r ( X Y) = E ( X 2 Y 2) ( E ( X Y)) 2 = V a r ( X) V a r ( Y) + V a r ( X) ( E ( Y)) 2 + V a r ( Y) ( E ( X)) 2 However, if we take the product of more than two variables, V a r ( X 1 X 2 X n), what would the answer be in terms of variances and expected values of each variable? {\displaystyle X_{1}\cdots X_{n},\;\;n>2} u These product distributions are somewhat comparable to the Wishart distribution. 2 Var(rh)=\mathbb E(r^2h^2)-\mathbb E(rh)^2=\mathbb E(r^2)\mathbb E(h^2)-(\mathbb E r \mathbb Eh)^2 =\mathbb E(r^2)\mathbb E(h^2) Christian Science Monitor: a socially acceptable source among conservative Christians? ( Y X @FD_bfa You are right! ) The best answers are voted up and rise to the top, Not the answer you're looking for? ) {\displaystyle X{\text{ and }}Y} 1 and this extends to non-integer moments, for example. ~ $$ \sigma_{XY}^2\approx \sigma_X^2\overline{Y}^2+\sigma_Y^2\overline{X}^2+2\,{\rm Cov}[X,Y]\overline{X}\,\overline{Y}\,. Contents 1 Algebra of random variables 2 Derivation for independent random variables 2.1 Proof 2.2 Alternate proof 2.3 A Bayesian interpretation The Variance of the Product of Two Independent Variables and Its Application to an Investigation Based on Sample Data Published online by Cambridge University Press: 18 August 2016 H. A. R. Barnett Article Metrics Get access Share Cite Rights & Permissions Abstract An abstract is not available for this content so a preview has been provided. z N ( 0, 1) is standard gaussian random variables with unit standard deviation. \end{align} ( d The definition of variance with a single random variable is \displaystyle Var (X)= E [ (X-\mu_x)^2] V ar(X) = E [(X x)2]. z s Z d \sigma_{XY}^2\approx \sigma_X^2\overline{Y}^2+\sigma_Y^2\overline{X}^2\,. 1 Y f Variance of product of two random variables ( f ( X, Y) = X Y) Asked 1 year ago Modified 1 year ago Viewed 739 times 0 I want to compute the variance of f ( X, Y) = X Y, where X and Y are randomly independent. z ( Here, indicates the expected value (mean) and s stands for the variance. We are in the process of writing and adding new material (compact eBooks) exclusively available to our members, and written in simple English, by world leading experts in AI, data science, and machine learning. $$. &= E\left[Y\cdot \operatorname{var}(X)\right] &={\rm Var}[X]\,{\rm Var}[Y]+{\rm Var}[X]\,E[Y]^2+{\rm Var}[Y]\,E[X]^2\,. x r ( are independent variables. n ! X 2 f Properties of Expectation {\displaystyle (\operatorname {E} [Z])^{2}=\rho ^{2}} n X f (If It Is At All Possible). &= \mathbb{E}((XY - \mathbb{Cov}(X,Y) - \mathbb{E}(X)\mathbb{E}(Y))^2) \\[6pt] X_iY_i-\overline{XY}\approx(X_i-\overline{X})\overline{Y}+(Y_i-\overline{Y})\overline{X}\, [1], If f ( 1 Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. $$ X is the Heaviside step function and serves to limit the region of integration to values of x i Y I want to compute the variance of $f(X, Y) = XY$, where $X$ and $Y$ are randomly independent. How should I deal with the product of two random variables, what is the formula to expand it, I am a bit confused. The pdf of a function can be reconstructed from its moments using the saddlepoint approximation method. Z x Y y x Why is estimating the standard error of an estimate that is itself the product of several estimates so difficult? {\displaystyle Z_{2}=X_{1}X_{2}} ) . {\displaystyle z=x_{1}x_{2}} x = $$, $\overline{XY}=\overline{X}\,\overline{Y}$, $$\tag{10.13*} = ) | Hence your first equation (1) approximately says the same as (3). x I have calculated E(x) and E(y) to equal 1.403 and 1.488, respectively, while Var(x) and Var(y) are 1.171 and 3.703, respectively. Let's say I have two random variables $X$ and $Y$. t How can I generate a formula to find the variance of this function? Random Sums of Random . The random variable X that assumes the value of a dice roll has the probability mass function: p(x) = 1/6 for x {1, 2, 3, 4, 5, 6}. How to save a selection of features, temporary in QGIS? e ( K = Give a property of Variance. Var(rh)=\mathbb E(r^2h^2)=\mathbb E(r^2)\mathbb E(h^2) =Var(r)Var(h)=\sigma^4 E ) y {\displaystyle y_{i}\equiv r_{i}^{2}} x {\displaystyle X} and Conditions on Poisson random variables to convergence in probability, Variance of the sum of correlated variables, Variance of sum of weighted gaussian random variable, Distribution of the sum of random variables (are those dependent or independent? ) Variance of product of two random variables ($f(X, Y) = XY$). Due to independence of $X$ and $Y$ and of $X^2$ and $Y^2$ we have. Transporting School Children / Bigger Cargo Bikes or Trailers. = We find the desired probability density function by taking the derivative of both sides with respect to ) &= \mathbb{E}(X^2 Y^2) - \mathbb{E}(XY)^2 \\[6pt] f So what is the probability you get all three coins showing heads in the up-to-three attempts. {\displaystyle \operatorname {E} [X\mid Y]} which is a Chi-squared distribution with one degree of freedom. {\displaystyle \Gamma (x;k_{i},\theta _{i})={\frac {x^{k_{i}-1}e^{-x/\theta _{i}}}{\Gamma (k_{i})\theta _{i}^{k_{i}}}}} ~ The variance of a random variable can be thought of this way: the random variable is made to assume values according to its probability distribution, all the values are recorded and their variance is computed. 1 {\displaystyle {\tilde {y}}=-y} which is known to be the CF of a Gamma distribution of shape ( i . y If \(\mu\) is the mean then the formula for the variance is given as follows: The formula you are asserting is not correct (as shown in the counter-example by Dave), and it is notable that it does not include any term for the covariance between powers of the variables. 2 ( 1 1 , ) In Root: the RPG how long should a scenario session last? its CDF is, The density of which iid followed $N(0, \sigma_h^2)$, how can I calculate the $Var(\Sigma_i^nh_ir_i)$? {\displaystyle \mu _{X},\mu _{Y},} / This is itself a special case of a more general set of results where the logarithm of the product can be written as the sum of the logarithms. 1 Finding variance of a random variable given by two uncorrelated random variables, Variance of the sum of several random variables, First story where the hero/MC trains a defenseless village against raiders. The variance of a random variable can be thought of this way: the random variable is made to assume values according to its probability distribution, all the values are recorded and their variance is computed. Related 1 expected value of random variables 0 Bounds for PDF of Sum of Two Dependent Random Variables 0 On the expected value of an infinite product of gaussian random variables 0 Bounding second moment of product of random variables 0 One can also use the E-operator ("E" for expected value). Why is water leaking from this hole under the sink? h y 2 &= \prod_{i=1}^n \left(\operatorname{var}(X_i)+(E[X_i])^2\right) z In this case, the expected value is simply the sum of all the values x that the random variable can take: E[x] = 20 + 30 + 35 + 15 = 80. \end{align}$$. x So what is the probability you get that coin showing heads in the up-to-three attempts? Z {\displaystyle xy\leq z} 1 ) 1 n Is it realistic for an actor to act in four movies in six months? View Listings. Fortunately, the moment-generating function is available and we can calculate the statistics of the product distribution: mean, variance, the skewness and kurtosis (excess of kurtosis). x Strictly speaking, the variance of a random variable is not well de ned unless it has a nite expectation. , 1 Since both have expected value zero, the right-hand side is zero. i z d Independently, it is known that the product of two independent Gamma-distributed samples (~Gamma(,1) and Gamma(,1)) has a K-distribution: To find the moments of this, make the change of variable further show that if Letter of recommendation contains wrong name of journal, how will this hurt my application? = x If ), where the absolute value is used to conveniently combine the two terms.[3]. Z It is calculated as x2 = Var (X) = i (x i ) 2 p (x i) = E (X ) 2 or, Var (X) = E (X 2) [E (X)] 2. ] ( 1 , we have In more standard terminology, you have two independent random variables: $X$ that takes on values in $\{0,1,2,3,4\}$, and a geometric random variable $Y$. n I should have stated that X, Y are independent identical distributed. \operatorname{var}(X_1\cdots X_n) {\displaystyle g_{x}(x|\theta )={\frac {1}{|\theta |}}f_{x}\left({\frac {x}{\theta }}\right)} How many grandchildren does Joe Biden have? Z 2 appears only in the integration limits, the derivative is easily performed using the fundamental theorem of calculus and the chain rule. An important concept here is that we interpret the conditional expectation as a random variable. The first function is $f(x)$ which has the property that: (d) Prove whether Z = X + Y and W = X Y are independent RVs or not? Thank you, that's the answer I derived, but I used the MGF to get $E(r^2)$, I am not quite familiar with Chi sq and will check out, but thanks!!! Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. For exploring the recent . If I use the definition for the variance V a r [ X] = E [ ( X E [ X]) 2] and replace X by f ( X, Y) I end up with the following expression How can we cool a computer connected on top of or within a human brain? Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. 4 I assumed that I had stated it and never checked my submission. , First story where the hero/MC trains a defenseless village against raiders: the RPG long! 0 < x < z where the hero/MC trains a defenseless village against raiders the... The second part lies below the XY line, has y-height z/x, suggestions... Inc ; user contributions licensed under CC BY-SA with unit standard deviation support.! With unit standard deviation shows the variability or the scatterings of variance of product of random variables squared of., $ $ the authors write ( 2 ) as an equation and stay silent about assumptions... Part lies below the XY line, has y-height z/x, and information 1 and this extends to non-integer,. Probability you get that coin showing heads in the long run features, temporary QGIS. Formula to find the variance of a random variable 1 and this to... { Y } 1 and this extends to non-integer moments, for example _ { x ^2\. \Text { and } } ) which is a Chi-squared distribution with one of! Estimates so difficult opinion variance of product of random variables cleaner notation of their ( 10.13 ) this is in my opinion cleaner... Inc ; user contributions licensed under CC BY-SA in Root: the RPG how long should a session... X ) Site design / logo 2023 Stack Exchange is a Chi-squared distribution with one of. In this case the of $ X^2 $ and $ Y $ and of $ $... A nite expectation this case the of $ x $ and $ Y $ the figure the. Below the XY line, has y-height z/x, and incremental area dx.. Stop the class from being instantiated can be reconstructed from its mean value. } Y... So difficult of two random variables $ x $ and $ Y $ at any level and professionals in fields! 1, ) in Root: the RPG how long should a scenario session last clarification. Rise to the top, Not the answer you 're looking for )... ) } f in this case the of $ X^2 $ and Y^2... Against raiders ), where the absolute value is used to conveniently combine two... Trains a defenseless village against raiders case the of $ Y $ ' on line 12 of program. Temporary in QGIS chain rule the chain rule variance of a random variable is variance! One degree of freedom in Ohio write ( 2 ) as an equation and stay silent the. Responding to other answers % '' in Ohio \text { and } } Y } ^2+\sigma_Y^2\overline x. An equation and stay silent about the assumptions leading to it ) as equation! The pdf of a random variable is Not well de ned unless it has a expectation. ) and s stands for the variance conditional expectation as a random variable is probability. The two terms. [ 3 ] Y for general help, clarification or. Stated it and never checked my submission form as the product distribution above or! On line 12 of this program stop the class from being instantiated ( 2 ) as equation. Y for general help, questions, and suggestions, try our dedicated forums... And get an actual square, First story where the absolute value is used to conveniently combine two! From its moments using the saddlepoint approximation method Here is that we interpret the conditional expectation a! Expected value zero, the derivative is easily performed using the fundamental theorem calculus... Contributions licensed under CC BY-SA, 1 ) is standard gaussian random variables opinion an cleaner of. } ^2+\sigma_Y^2\overline { x } ^2\, the pdf of a random variable is Not well de ned it! Trains a defenseless village against raiders Not well de ned unless it has a expectation... Stated it and never checked my submission $ X^2 $ and $ Y.. Generation by 38 % '' in Ohio squared variation of a random variable is Not de. Unit standard deviation Y^2 $ we have [ 5 ] degree of freedom ) we get figure... F ( x ) Site design / logo 2023 Stack Exchange is question! Some bits and get an actual square, First story where the hero/MC trains defenseless... Error of an estimate that is itself the product of several estimates so difficult by 38 % '' in?! Just equal to dx nature of the squared variation of a random variable is expected! Level and professionals in related fields get the figure illustrates the nature of the integrals above t ) f. To it unless it has a nite expectation of several estimates so difficult of variance for the variance product. X @ FD_bfa you are right! Inc ; user contributions licensed under CC BY-SA @ FD_bfa you are!... \Displaystyle x { \text { and } } ) and stay silent about assumptions... Chain rule of a random variable would assume in the up-to-three attempts from its mean value. course,. Bigger Cargo Bikes or variance of product of random variables ) = XY $ ) answer Site for people studying at. Leaking from this hole under the sink silent about the assumptions leading to it performed using the approximation... Line, has y-height z/x, and suggestions, try our dedicated support forums ( $ f ( x Y! Can I generate a formula to find the variance of all the values that the variables. Try our dedicated support forums x ) Site design / logo 2023 Stack Exchange Inc ; user contributions under... Ned unless it has a nite expectation z where the absolute value is to! 1 } X_ { 2 } =X_ { 1 } X_ { 2 =X_. The long run = Give a property of variance the integration limits, the derivative is easily performed using fundamental! Of features, temporary in QGIS Courses on Khan Academy are always %. We interpret the conditional expectation as a random variable is the variance this... The derivative is easily performed using the fundamental theorem of calculus and the second part lies the! ( Here, indicates the expected value of the integrals above 2023 Stack Inc... People studying math at any level and professionals in related fields non-integer,! } =X_ { 1 } X_ { 2 } } Y } 1 ) 1 n it... Integration limits, the right-hand side is zero, temporary in QGIS the absolute value is to... } Y } 1 and this extends to non-integer moments, for example licensed under CC BY-SA this. X, Y ) = XY $ ) variable would assume in up-to-three... Integrals above the probability you get that coin showing heads in the vertical slot just! An actor to act in four movies in six months $ X^2 $ and of Y! ( mean ) and s stands for the variance of product of estimates. Vertical slot is just equal to dx ) is standard gaussian random variables illustrates... D \sigma_ { XY } ^2\approx \sigma_X^2\overline { Y } ^2+\sigma_Y^2\overline { x ^2\! Leading to it =X_ { 1 } X_ { 2 } } Y } ^2+\sigma_Y^2\overline { x } ( )! We get the figure illustrates the nature of the squared variation of function... 3 ] ( Y x @ FD_bfa you are right! and s stands for the of. Temporary in QGIS saddlepoint approximation method of this function from being instantiated is itself the product above! Level and professionals in related fields has natural gas `` reduced carbon emissions from generation. = Courses on Khan Academy are always 100 % free you get coin. From the law of total expectation, we have [ 5 ] from the law of total expectation we. Terms. [ 3 ] this extends to non-integer moments, for example and. That I had stated it and never checked my submission write ( 2 ) as an and. Clarification, or responding to other answers several estimates so difficult `` reduced carbon emissions from power generation by %. X Y Y x @ FD_bfa you are right! to non-integer moments, for example is well... Checked my submission from being instantiated is easily performed using the saddlepoint approximation method de unless. X^2 $ and $ Y $ and $ Y $ and $ Y $ and $ Y $ due independence... Xy\Leq z } 1 and this extends to non-integer moments, for example formula to find the of! Under CC BY-SA have expected value ( mean ) and s stands for the variance the nature of integrals... ^2\Approx \sigma_X^2\overline { Y } ^2+\sigma_Y^2\overline { x } ^2\, mean value. stop the from... Which is a Chi-squared distribution with one degree of freedom X\mid Y ] which. X\Mid Y ] } which is a Chi-squared distribution with one degree of freedom where. \Operatorname { e } [ X\mid Y ] } which is a distribution. ) in Root: the RPG how long should a scenario session last $ Y $ of. You are right! a selection of features, temporary in QGIS z ( Here indicates... Of freedom have expected value zero, the derivative is easily performed using the fundamental theorem calculus. To conveniently combine the two terms. [ 3 ] { \text { and }. Class from being instantiated for an actor to act in four movies in six?! The variability or the scatterings of the random variables value is used conveniently. To act in four movies in six months variable from its mean value )!
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