Linked Questions
19 questions linked to/from Variance of product of multiple independent random variables
5
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3
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81
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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)
...
- 2,119
3
votes
1
answer
114
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
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?
0
votes
1
answer
39
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exercise autocovariance function
I don't know how to obtain the autocovariance function of the following process, having a multiplication makes it difficult for me.
$X_t = Z_t + \theta Z_tZ_{t-1}$
with $Z_i \sim N(0, \sigma^2)$ (...
0
votes
0
answers
2k
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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, ...
- 31
4
votes
1
answer
903
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?
5
votes
1
answer
250
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
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 ...
- 67
1
vote
0
answers
5k
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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:
...
- 111
7
votes
1
answer
102k
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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?
- 71
2
votes
0
answers
210
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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
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...
$$\{X_t\} = Y_t(1-Y_{t-1})Z_t$$...
- 13
5
votes
0
answers
117
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 ...
- 51
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 + ...
0
votes
0
answers
93
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 ...
- 101