Hypergeometric Distribution

Probability · Axiom Academy

LESSON Hypergeometric Distribution Sampling without replacement from a finite population A random variable X follows a Hypergeometric distribution if: Population has N total items: K successes, N-K failures Draw n items without replacement X counts the number of successes in the sample Parameters: N (population), K (successes in pop), n (sample size) The PMF counts favorable outcomes over total possible outcomes: 3. Expected Value and Variance The mean matches the Binomial, but variance has a finite population correction: E[X] = n(K/N) = np where p = K/N Var(X) = np(1-p) × (N-n)/(N-1) Factor (N-n)/(N-1) < 1 reduces variance due to no replacement

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