Math1313-Section8.4-Blank

Math1313-Section8.4-Blank - Section 8.4 The Binomial...

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Section 8.4 The Binomial Distribution A binomial experiment has the following properties: 1. The number of trials is fixed. 2. There are two outcomes of the experiment: Success, with probability p and Failure, with probability q . Note: p + q = 1. 3. The probability of success in each trial is the same. 4. The trials are independent of each other. Experiments with two outcomes are called Bernoulli trials or Binomial trials . Finding the Probability of an Event of a Binomial Experiment In a binomial experiment in which the probability of success in any trial is p , the probability of exactly x successes in n independent trials is given by x n x q p x n C x X P = = ) , ( ) ( X is called a binomial random variable and its probability distribution is called a binomial probability distribution . Example 1: Let the random variable X denote the number of girls in a two-child family. If the probability of a female birth is 0.5, construct the binomial distribution associated with this experiment. Mean, Variance and Standard Deviation of a Random Variable

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Math1313-Section8.4-Blank - Section 8.4 The Binomial...

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