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# Let $X$ be a random variable whose possible values $x_1, x_2, ..., x_n$ occur with probabilities $p(x_1), p(x_2), ..., p(x_n)$ respectively. Then if $\mu$ is the mean of $X$, what is the standard deviation of $X$?

Standard Deviation = $\sqrt Variance$.

Variance = $\sum_{i=1}^{n}p_i\;x_i^2-\mu^2$

Therefore Standard Deviation = $\sqrt (\sum_{i=1}^{n}p_i\;x_i^2-\mu^2)$