post11 - STAT 511-2 Spring 2012 Lecture 11 Feb 3, 2012 Jun...

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1 STAT 511-2 Spring 2012 Lecture 11 Feb 3, 2012 Jun Xie 3.4 The binomial probability distribution An experiment that satisfies the following conditions is called a binomial experiment. 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. 4. The probability of success P ( S ) is constant from trial to trial; we denote this probability by p. Definition The binomial random variable X associated with a binomial experiment consisting of n trials is defined as X = the number of S among the n trials We will often write X ~ Bin( n , p ) to indicate that X is a binomial rv based on n trials with success probability p. The pmf of X ~ Bin( n , p ) is p(x)= = ° ± ² p x (1-p) n-x . Example 31
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This note was uploaded on 02/20/2012 for the course STAT 511 taught by Professor Bud during the Fall '08 term at Purdue University-West Lafayette.

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post11 - STAT 511-2 Spring 2012 Lecture 11 Feb 3, 2012 Jun...

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