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Proof that $\mathbb{E}(S_n ^2) = \sigma ^2$

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#statistics #estimation #variance
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Prove that $\min_{a \in \Bbb R} E((X - a)^2) = Var(X)$

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#probability #variance
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Is the following calculation of $\mathrm{Var}\left(\sum\limits_{i=0}^{k}(c_{x1}+c_{x2}X_i)(c_{y1}+c_{y2}Y_i)\right)$ correct?

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#probability #variance
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Suppose $X_1\cdots X_n$ are correlated normal random variables...

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#probability #expectation #covariance #variance
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Conditional Variance For Discrete & Continous Random Variable X

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#statistics #variance
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Decomposition of variance

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#variance
1.8k
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Simple Random Walk, proving variance of the walk at a stopping time

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#probability #expectation #random-walk #stopping-times #variance
24
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Sum of different distributed r.v.

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#expectation #variance #bivariate-distributions
288
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Variance of ratio

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#probability #standard-deviation #ratio #variance
1.3k
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Calculating Variance when there is a random variable in the exponent

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#probability #probability-theory #variance
163
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Local central limit theorem for sum of random variables (size of unrooted trees) with infinite variance

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#trees #central-limit-theorem #variance
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Variance of 1/X

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#probability #variance #exponential-distribution
1.2k
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Minimum variance of estimator

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#statistics #means #variance
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Poisson Distribution -- Why No Need To Measure Standard Deviation?

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#standard-deviation #poisson-distribution #variance
256
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Supermartingale variance bound?

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#probability #probability-theory #reference-request #martingales #variance

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