Discrete random variables

Learning objectives

Draw up the probability distribution table of a discrete random variable from a described situation, using Σp = 1 to find unknown probabilities

Calculate E(X) = Σxp and Var(X) = Σx²p − [E(X)]² from a probability distribution

Use the binomial distribution B(n, p), with P(X = r) = ⁿCᵣ pʳ(1 − p)ⁿ⁻ʳ, mean np and variance np(1 − p), including cumulative probabilities such as P(X ≥ 2)

Use the geometric distribution Geo(p), with P(X = r) = p(1 − p)ʳ⁻¹ for r = 1, 2, 3, …, P(X > r) = (1 − p)ʳ and mean 1/p

Decide whether a binomial or a geometric model suits a context, and state the assumptions of independence and constant probability in that context