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The Binomial Probability Distribution

The Binomial Probability Distribution Copyright Cengage Learning. All rights reserved. The Binomial Probability Distribution There are many experiments that conform either exactly or approximately to the following list of requirements: 1. The experiment consists of a sequence of n smaller experiments called trials, where n is fixed in advance of the experiment. 2. Each trial can result in one of the same two possible outcomes (dichotomous trials), which we generically denote by success (S) and failure (F). 3. The trials are independent, so that the outcome on any particular trial does not influence the outcome on any other trial. 2. The Binomial Probability Distribution 4. The Probability of success P(S) is constant from trial to trial; we denote this Probability by p.

distribution. The mean value of a Bernoulli variable is = p, so the expected number of S’s on any single trial is p. Since a binomial experiment consists of n trials, intuition suggests that for X ~ Bin(n, p), E(X) = np, the product of the

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