The Bernoulli Distribution

• We use the Bernoulli distribution when we have an experiment which can result in one of two outcomes – One outcome is labeled “success, ” and the other outcome is l b l d “f il ”a e e a ure – The probability of a success is denoted by p. The probability of a failure is then 1 – p • Such a trial is called a Bernoulli trial with success probability p Statistics-Berlin Chen 3 Examples 1. The simplest Bernoulli trial is the toss of a coin. The two outcomes are heads and tails. If we define heads to be the success outcome, then p is the probability that th i h d F f i i e co n comes up ea s. or a a r co n, p = f2. Another Bernoulli trial is a selection o a component from a population of components, some of which are defective If we define “success ” to be a defective. component, then p is the proportion of defective components in the population Statistics-Berlin Chen 4 X ~ Bernoulli(p) • For any Bernoulli trial, we define a random variable X as follows: – If the experiment results in a success, then X = 1. Otherwise,