Expected value and variance of probability distribution
Let the probability distribution of random variable $X$ be
| $x$ | $x_1$ | $x_2$ | $\cdots$ | $x_n$ |
|---|---|---|---|---|
| $P(X=x)$ | $p_1$ | $p_2$ | $\cdots$ | $p_n$ |
Formula
The expected value of $X$ is given by
$E(X) =\mu = \sum_x x*P(X=x)$
The variance of $X$ is given by
$V(X) =\sigma^2 = E(X^2) -[E(X)]^2$
where $E(X^2) = \sum_x x^2*P(X=x)$
