## 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 $E(X^2) = \sum_x x^2*P(X=x)$