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### Var(XY), if X and Y are independent random variables [duplicate]

if X and Y are independent Random variable then what is the variance of XY?
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### How to calculate variance or standard deviation for product of two normal distributions? [duplicate]

For example if I have two multiplied distributions a * b: ...
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### Define $Var(XY)$ in terms of $E(X)$, $E(Y)$, $Var(X)$, $Var(Y)$ for Independent Random Variables $X$ and $Y$ [duplicate]

I currently know: $$Var(XY)=E(X^2Y^2)−[E(XY)]^2$$ $$=E(X^2)E(Y^2)−[E(X)]^2[E(Y)]^2$$ but I am lost where to go from there. I can vaguely see the the formula $Var(X)=E(X^2)-E(X)^2$ hidden somewhere, ...
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What is the formula for variance of product of dependent variables? In the case of independent variables the formula is simple: $${\rm var}(XY) = E(X^{2}Y^{2}) - E(XY)^{2} = {\rm var}(X){\rm var}(... • 113 14 votes 3 answers 6k views ### Variance of product of k correlated random variables What is the variance of the product of k correlated random variables? 13 votes 1 answer 7k views ### Variance of powers of a random variable Is it possible to derive a formula for variance of powers of a random variable in terms of expected value and variance of X?$$\operatorname{var}(X^n)= \,?$$and$$E(X^n)=\,?$$• 901 4 votes 1 answer 815 views ### Standard deviation/variance for the sum, product and quotient of two Poisson distributions What would be the standard deviation for A+B, AB and \frac{A}{B} for A and B Poisson distributed? 4 votes 1 answer 294 views ### Given that X and Y are normally distributed as N(0,3) and N(0,5) respectively, what is the expected value of (XY)^2? Given that X and Y are independent and normally distributed as N(0,3) and N(0,5) respectively, what is the expected value of (XY)^2? 1 vote 2 answers 697 views ### If you know a normal distribution's population variance, does a sample variance tell you nothing about the sample's mean's confidence interval? If I understand correctly (which I might not), if I know a normal distribution's population variance but not its population mean, and take just one sample consisting of three measurements, then no ... • 67 5 votes 1 answer 237 views ### Point estimator for product of independent RVs Let X and Y be two independent random variables. Given an (iid) random sample of size n of X and a random sample of size n of Y, what is a good way to estimate the mean of their product, ... • 309 4 votes 1 answer 293 views ### Why is estimating the standard error of an estimate that is itself the product of several estimates so difficult? Singer and Willett (2003) write the following about estimating the standard errors of estimated survival probabilities within the context of discrete time event history models (e.g. logit hazard ... • 28.3k 0 votes 2 answers 195 views ### Variance of the difference of products of iid sequences So suppose you have two sequences \{Y_t\} and \{Z_t\} and they are both iid and independent from each other. Now suppose I have a time series \{X_t\} such that...$$\{X_t\} = Y_t(1-Y_{t-1})Z_t$$... • 13 3 votes 2 answers 170 views ### What is V(X^t) for any t when only E(X) and Var(X) are known and X is assumed normal? Summary I'm trying to calculate Var(X^t) where t is the number of periods using only the following known parameters: E(X) and Var(X). X is a random variable and is the return factor (1 + ... 3 votes 1 answer 84 views ### What is the conditional \operatorname{Var}(XY|Y) given that X and Y are independent? What is the conditional \operatorname{Var}(XY|Y) given X and Y are independent? Is it:$$\operatorname{Var}(XY|Y)= Y^2\operatorname{Var}(X|Y) = Y^2\operatorname{Var}(X)?
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I know that the sum of two Wrapped Normal Variables is a Wrapped Normal Variable. In particular, if $\theta_1 \sim WN(\mu_1, \rho_1)$ and $\theta_2 \sim WN(\mu_2, \rho_2)$, then \$\theta_1 + \theta_2 \...