What is Bernoulli distribution?

A Bernoulli trial is an experiment with two outcomes, success (probability $p$) and failure ($q = 1 - p$). The indicator $X$ of success ($X = 1$ on success, $0$ on failure) follows the Bernoulli distribution $\mathcal B(p)$:

(Indeed $\E(X) = p$, $\E(X^2) = p$, and König–Huygens gives $\V(X) = p - p^2$.)