The Geometric Distribution

A discrete random variable X is said to have a geometric distribution if it has a probability density function (p.d.f.) of the form:

• P(X = x) = q^(x-1)p, where q = 1 - p

If X has a geometric distribution with parameter p, we write X ~ Geo(p)

Expectation and Variance

If X ~ Geo(p), then:

• E(X) = 1/p

• Var(X) = q/p², where q = 1 – p

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