Linked Questions
18 questions linked to/from Variance of product of multiple independent random variables
7
votes
1
answer
96k
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?
- 71
0
votes
0
answers
4k
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:
...
- 101
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, ...
- 31
41
votes
2
answers
67k
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:
$$ {\rm var}(XY) = E(X^{2}Y^{2}) - E(XY)^{2} = {\rm var}(X){\rm var}(...
- 113
14
votes
3
answers
6k
views
Variance of product of k correlated random variables
What is the variance of the product of $k$ correlated random variables?
- 185
13
votes
1
answer
7k
views
Variance of powers of a random variable
Is it possible to derive a formula for variance of powers of a random variable in terms of expected value and variance of X?
$$\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)?$$
- 33
2
votes
0
answers
204
views
Is the product of two Wrapped Normal Variables a Wrapped Normal Variable? [closed]
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 \...
- 151