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Unformatted text preview: Chapter 5: Some Discrete Probability Distributions 71 CHAPTER 5 SOME DISCRETE PROBABILITY DISTRIBUTIONS ( But well only cover one of them ) In this chapter we introduce a discrete probability distribution that is commonly used in practice. BINOMIAL DISTRIBUTION Consider a statistical experiment that has exactly two outcomes. (Such an experiment is called a Bernoulli experiment.) Tossing a coin Passing / failing a test Winning a contest Producing a defective / non-defective item In each case, we designate one outcome to be a success and the other outcome to be a failure . Suppose we repeat this experiment n times such that each trial is independent of the other trials (i.e., the probability of success in one trial does not depend on the outcome of any other trial). Let X be the number of successes observed among the n trials. Then X is said to follow a binomial distribution. Example : Suppose a fair coin is flipped ten times. Find the probability that heads appears exactly three times. Consider the following sequences of coin flips, each of which has exactly 3 heads and 7 tails: P(H,H,H,T,T,T,T,T,T,T) = () 10 P(T,T,T,T,T,T,T,H,H,H) = () 10 P(H,T,T,H,T,T,H,T,T,T) = () 10 etc....
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