Cue Column:

• What defines a Bernoulli trial?
• What is P(X = r)?
• What are mean and variance?

Note Column: A Bernoulli trial has exactly two outcomes: success (probability p) and failure (probability q = 1 - p). In n independent Bernoulli trials, X = number of successes follows the Binomial distribution: P(X = r) = C(n,r) * $p^r$ * q^(n-r) for r = 0, 1, ..., n. Mean E(X) = np, Variance Var(X) = npq, Standard deviation = sqrt(npq). The probabilities sum to (p+q)^n = 1.

Summary: Binomial distribution models repeated independent trials with fixed success probability. The formula, mean, and variance are direct applications of the binomial expansion.