Linked Questions
22 questions linked to/from Variance of product of multiple independent random variables
7
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1
answer
126k
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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
1
vote
0
answers
7k
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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
0
votes
0
answers
4k
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
43
votes
2
answers
73k
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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:
$$ \operatorname{var}(XY) = E(X^2Y^2) - E(XY)^2 = \operatorname{var}(X) \...
- 133
29
votes
3
answers
34k
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What's the difference between variance scaling initializer and xavier initializer?
In Tensorflow's implementation of ResNet, I find they use variance scaling initializer, I also find xavier initializer is popular. I don't have too much experience on this, which is better in practice?...
- 653
14
votes
3
answers
6k
views
Variance of product of k correlated random variables
What is the variance of the product of $k$ correlated random variables?
- 185
13
votes
1
answer
8k
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Variance of powers of a random variable
Is it possible to derive a formula for variance of powers of a random variable in terms of expected value and variance of X?
$$\operatorname{var}(X^n)= \,?$$
and
$$E(X^n)=\,?$$
- 1,051
5
votes
1
answer
1k
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Standard deviation/variance for the sum, product and quotient of two Poisson distributions
What would be the standard deviation for $A+B$, $AB$ and $\frac{A}{B}$ for $A$ and $B$ Poisson distributed?
4
votes
1
answer
315
views
Given that X and Y are normally distributed as N(0,3) and N(0,5) respectively, what is the expected value of (XY)^2?
Given that X and Y are independent and normally distributed as N(0,3) and N(0,5) respectively, what is the expected value of (XY)^2?
5
votes
1
answer
321
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Point estimator for product of independent RVs
Let $X$ and $Y$ be two independent random variables. Given an (iid) random sample of size $n$ of $X$ and a random sample of size $n$ of $Y$, what is a good way to estimate the mean of their product, $...
- 359
1
vote
2
answers
835
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If you know a normal distribution's population variance, does a sample variance tell you nothing about the sample's mean's confidence interval?
If I understand correctly (which I might not), if I know a normal distribution's population variance but not its population mean, and take just one sample consisting of three measurements, then no ...
- 67
4
votes
1
answer
303
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Why is estimating the standard error of an estimate that is itself the product of several estimates so difficult?
Singer and Willett (2003) write the following about estimating the standard errors of estimated survival probabilities within the context of discrete time event history models (e.g. logit hazard ...
- 29.9k
3
votes
1
answer
292
views
What is the conditional $\operatorname{Var}(XY|Y)$ given that $X$ and $Y$ are independent?
What is the conditional $\operatorname{Var}(XY|Y)$ given $X$ and $Y$ are independent?
Is it:
$$\operatorname{Var}(XY|Y)= Y^2\operatorname{Var}(X|Y) = Y^2\operatorname{Var}(X)?$$
- 33
5
votes
3
answers
137
views
Confidence intervals calculated from other confidence intervals (binomial problem)?
In a binomial experiment, I have an estimate for the probability of 3 independent events A, B & C, each with a 95% confidence interval.
(Trivial example values)
...
- 2,129
0
votes
2
answers
202
views
Variance of the difference of products of iid sequences
So suppose you have two sequences $\{Y_t\}$ and $\{Z_t\}$ and they are both iid and independent from each other. Now suppose I have a time series $\{X_t\}$ such that...
$$\{X_t\} = Y_t(1-Y_{t-1})Z_t$$...
- 13
3
votes
2
answers
194
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 + ...
2
votes
0
answers
240
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
0
votes
1
answer
101
views
Why the standard deviation of the BERT weight initialization is 0.02 by default
The purpose of weight initialization in the neural network is to keep the variance of calculation output in the layers to 1.0, and it depends on the calculations involved in the layers.
Initializing ...
- 1,468
5
votes
0
answers
118
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
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
0
votes
1
answer
48
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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
51
views
Variance of powers of a standard normal random variable
To predict growth of money in a stock market I try to calculate expected return over a longer timeframe (e.g. 30 years) with a confidence interval. The simple math of taking an average stock market ...
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