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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.
37
votes
Accepted
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. …
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
$$
\mathbb{V}(X) = \frac{1}{N …
1
vote
Binomial variance: method proof
Part one is clear.
$$
\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 …