Linked Questions

1
vote
1answer
35k 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?
0
votes
0answers
2k 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: ...
0
votes
0answers
795 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, ...
37
votes
2answers
56k 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}(...
14
votes
3answers
5k views

Variance of product of k correlated random variables

What is the variance of the product of $k$ correlated random variables?
10
votes
1answer
5k 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 $$E(X^n)=\,?$$
4
votes
1answer
202 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
1answer
262 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 ...
5
votes
1answer
71 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, $...
1
vote
2answers
235 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 ...
3
votes
2answers
154 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 + ...
0
votes
2answers
144 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... $$\{X_t\} = Y_t(1-Y_{t-1})Z_t$$...
2
votes
0answers
152 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 \...
5
votes
0answers
97 views

How can I calculate the probability that the product of two independent random variables does not exceed $L$?

I have one variable, $X$, which is provided hourly for a period of one month (720 total values in the series). I have another variable, $Y$, which is provided quarterly (for which I am provided the ...
0
votes
0answers
85 views

Finding the best predictor Brownian motion

I want to find the best predictor of $(B_3-B_2)(B_4-B_{\pi})$ given an observation of $B_1$ Where $B_t$ is brownian motion for time $t \geq 0$. I am not sure how to approach this. I know it will be ...

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