Binomial Distribution

Probability · Axiom Academy

Counting successes in n independent Bernoulli trials A random variable X follows a Binomial distribution with parameters n and p if: n independent trials are performed Each trial has probability p of success X counts the total number of successes Parameters: n ≥ 1 (integer), 0 ≤ p ≤ 1 The PMF calculates the probability of observing exactly k successes in n trials: 3. Expected Value and Variance The mean and variance have intuitive interpretations: E[X] = np: On average, we expect np successes Var(X) = np(1-p): Variance scales linearly with n

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