# Questions tagged [variance]

For questions regarding the variance of a random variable in probability, as well as the variance of a list or data in statistics.

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### Determining variance from sum of two random correlated variables

I understand that the variance of the sum of two independent normally distributed random variables is the sum of the variances, but how does this change when the two random variables are correlated?
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### Minimum mean squared error of an estimator of the variance of the normal distribution [duplicate]

I am trying to find the estimator of the variance $\sigma^2$ of a normal distribution with the minimum mean square error. From reading up, I know the unbiased estimator of the variance of a Guassian ...
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### If $m$ tickets are drawn out of $n$ tickets numbered $1$ to $n$, find $V(X)$ where $X$ is the sum of the numbers on tickets.

$m$ tickets are drawn out of $n$ tickets which are numbered from $1$ to $n$. If $X$ denote the sum of the numbers on the tickets drawn. Find $V(X)$. $X = X_1+X_2+...+X_m$ , if $X_i$ can be treated as ...
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### What is the largest possible variance of a random variable on $[0; 1]$?

What is the largest possible variance of a random variable on $[0; 1]$? It is evident that it does not exceed $1$, but I doubt, that $1$ is actually possible. The largest variance, for which I found ...
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### Unbiased estimator of the variance with known population size

The variance is defined as $$\sigma^2 = \frac{\sum_{i=1}^n (x_i - \bar x)^2}{n}$$ where, $\bar x = \frac{\sum_{i=1}^n x_i}{n}$ If someone wants to estimate this parameter from a sample (s)he must ...
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### MLE of variance minimising the mean squared error

While reading up on the derivation of a Maximum Likelihood Estimator for population variance, the MLE for Variance ends up being the biased sample variance, $\frac{n-1}{n}S^2$ where $S^2$ is the ...
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### how to interpret the variance of a variance?

I understand how to interpret variance, but, what is the physical meaning behind the variance of a variance? Does it relate to error bounds at all (e.g. confidence interval)?
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### compute confidence interval from “variance of the sample variance”?

(This question spawned from how to interpret the variance of a variance?) For a random variable having a normal distribution with zero mean, we know its sample variance (1.2) and also the variance of ...
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### Finding Variance from a joint moment generating function

The random vars X and Y have, for all real values of $T_1, T_2$, the joint mgf $M(T_1 , T_2) = \frac{1}{2} e^{T_1 +T_2} + \frac{1}{4} e^{2T_1 +T2} + \frac{1}{12}e^{T_2} + \frac{1}{6} e^{4T_1 +3T_2}$ ...
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### Why variance is not squared before scaling for rolling dice problem?

I am trying to calculate mean $E[Y]$ and variance $Var[Y]$ of sums, when rolling a dice of 6 outcomes $(1,2,3,4,5,6)$, 10 times. I get the mean as below. Mean of sums for 10 tosses \$ Y = 10X, \\ \...