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Unformatted text preview: 8.4: The Binomial Distribution Another important type of random variable for which we have a for- mula for P ( X = x ) is called the binomial random variable . If X is a binomial random variable, then it has the following charac- teristics: The experiment consists of a fixed number, n , of repeated trials. The outcome of each trial is classified as either a success, or as a failure. The outcome of any one trial is independent of the outcomes of the other trials. For each trial, the probability of success, p , and the probability of failure, q , are constant. The random variable X counts the number of successes. An example of a binomial random variable is the following. Consider the experiment where a coin is flipped 100 times, and where the ran- dom variable X counts the number of times heads is flipped. This is binomial, as there are a fixed number of trials ( n = 100 flips), with each flip characterized as a success (heads) or a failure (tails). The probability of success (probability of heads) is 0 . 5 for each flip, and the probability of failure (probability of tails) is 0 . 5 for each flip. The flips are independent, and the random variable X counts the number of successes (number of heads)....
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