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Unformatted text preview: MA/STAT416: Probability Lecture Notes Spring 2011 1 Chapter 6: Standard Discrete Distributions March 8, 2011 6 Binomial, Geometric, and Uniform Distributions 6.1 The Binomial Distribution Suppose a coin has probability of heads equals to p (not necessarily 1 2 ) is tossed n times. The coin is not a fair coin. Describe the distribution of X = number of heads. This is the binomial distribution with parameters n and p . X has B ( n,p ). P ( X = x ) = n x p x (1 p ) n x , x = 0 , 1 , 2 , ··· ,n. Theorem 1. If X has B ( n,p ) , then μ X = E ( X ) = np and var ( X ) = p np (1 p ) . Example 2 . A fair coin is tossed 5 times. Let X denote the number of heads obtained. Describe the distribution. Find the expected value and variance of X . Example 3 . A multiple choice examination has 25 questions, each having 5 choices. The passing grade is 10. Suppose a student, completely unprepared, chooses his answers randomly. What is his probability of passing? What is the most likely number of correct answers he gets? Example 4 . An insurance agent has 15 policy holders that are considered highrisk. Any one of them has a 2.5% probability of making a claim. Letone of them has a 2....
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This note was uploaded on 04/23/2011 for the course STAT 416 taught by Professor Staff during the Spring '08 term at Purdue.
 Spring '08
 Staff
 Binomial, Probability

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