Negative Binomial Distribution

Probability · Axiom Academy

LESSON Negative Binomial Distribution Number of trials until the r-th success A random variable X follows a Negative Binomial distribution with parameters r and p if: Independent trials are performed until r successes occur Each trial has probability p of success X counts the trial on which the r-th success occurs Parameters: r ≥ 1 (integer), 0 < p ≤ 1 To get the r-th success on trial k, we need exactly r-1 successes in first k-1 trials, then success on trial k: 3. Expected Value and Variance The mean and variance extend naturally from the Geometric distribution: E[X] = r/p: On average need r/p trials for r successes Var(X) = r(1-p)/p²: Variance scales linearly with r

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