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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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Difference between Variance and 2nd moment

$$ \mathbb{E}(X^n) = \text{raw moment}\\ \mathbb{E}\left[\left(X-\mathbb{E}(X)\right)^n\right] = \text{central moment} $$ where the 2nd central moments represents the variance. …
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4 votes

Generating a series with mean=0 and variance=1

Let us break this down $$ \mathbb{E}(X) = \frac{1}{N}\sum_{k=0}^Nx_k $$ So the mean is (relatively) easy as we just require $$ \sum_{k=0}^Nx_k = 0 $$ Then the variance is $$ \mathbb{V}(X) = \frac{1}{N …
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1 vote

Binomial variance: method proof

Part one is clear. $$ \left(\matrix{x \\ 2}\right) = \frac{x!\cdots}{2!(x-2)!} = \frac{x(x-1)}{2} = \frac{1}{2}x^2-\frac{1}{2}x $$ The pairs is useful relationship to get a solution for the expectatio …
Chinny84's user avatar
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