We now show the mean and variance of a Bernoulli distribution,
\[ p(x) = \begin {cases} \pi & \text{if } x = 1\\[0.5em] (1 - \pi) & \text{if } x = 0\\[0.5em] 0 & \text{otherwise} \end {cases} \]Bernoulli mean and variance
If a random variable \(X\) has a \(\BernoulliDistn(\pi)\) distribution, its mean and variance are
\[ E[X] = \pi \spaced{and} \Var(X) = \pi(1-\pi) \](Proved in full version)