Probability Distribution Formulas
Binomial: P(X=k) = C(n,k) * p^k * (1-p)^(n-k), Mean = np, Variance = np(1-p)
Negative Binomial: P(X=k) = C(k-1,r-1) * p^r * (1-p)^(k-r), Mean = r/p, Variance =
r(1-p)/p^2
Geometric: P(X=k) = (1-p)^(k-1) * p, Mean = 1/p, Variance = (1-p)/p^2
Poisson: P(X=k) = λ^k * e^(-λ) / k!, Mean = λ, Variance = λ
Notation: n = number of trials, k = successes, r = required successes, p = success
probability, λ = expected events
Definitions: Each distribution models different real-world events (success/failure,
trials until success, rare events, etc.)