Mathematical Methods · discrete RVs · manipulative

np for the centre, np(1−p) for the spread

n copies of a Bernoulli(p) trial. The mean adds: np. The variance adds: np(1−p) — a hill that peaks at p = ½.

P(X = k) μ = np Var vs p
μ = np
—
Var = np(1−p)
—

Binomial pmf

Variance as p moves

Parameters

10
0.30

Working