Linked Questions

7 votes
1 answer
102k views

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?
Dev's user avatar
  • 71
1 vote
0 answers
5k views

How to calculate variance or standard deviation for product of two normal distributions? [duplicate]

For example if I have two multiplied distributions a * b: ...
dereks's user avatar
  • 111
0 votes
0 answers
2k views

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, ...
BGrove's user avatar
  • 31
41 votes
2 answers
69k views

Variance of product of dependent variables

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}(...
Riga's user avatar
  • 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?
Jafar Mansouri's user avatar
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 $$E(X^n)=\,?$$
damla's user avatar
  • 931
4 votes
1 answer
910 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?
Abhinna Sundar's user avatar
4 votes
1 answer
302 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?
spicy_springroll's user avatar
1 vote
2 answers
727 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 ...
MCC's user avatar
  • 67
5 votes
1 answer
252 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, $...
rishai's user avatar
  • 309
4 votes
1 answer
298 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 ...
Alexis's user avatar
  • 28.5k
5 votes
3 answers
83 views

Confidence intervals calculated from other confidence intervals (binomial problem)?

In a binomial experiment, I have an estimate for the probability of 3 independent events A, B & C, each with a 95% confidence interval. (Trivial example values) ...
Dominic Comtois's user avatar
0 votes
2 answers
197 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... $$\{X_t\} = Y_t(1-Y_{t-1})Z_t$$...
JJ Stamp's user avatar
3 votes
1 answer
117 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: $$\operatorname{Var}(XY|Y)= Y^2\operatorname{Var}(X|Y) = Y^2\operatorname{Var}(X)?$$
fakerman's user avatar
3 votes
2 answers
175 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 + ...
Anthony Schmitz's user avatar

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