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Unformatted text preview: Lecture 12. The Poisson Random Variable How many chocolate chips? . What is the probability of getting k chocolate chips in a cookie if the average number of chips per cookie is λ ? You are to assume that the cookies have been cut out from an huge batch of cookie dough in which the chocolate chips are randomly distributed. Actually, we want to find the limit as the amount of dough approaches infinity. (Those of you who like chocolate-chip-cookies should enjoy this.) It turns out that the probability is given by a famous pmf, called the Poisson distribution . We shall derive the formula for it from the binomial distribution. Setting up the problem . Let us begin by deciding to measure the dough in units of weight such that one cookie weighs one unit. Assume the amount of dough is d —that is, we have enough dough to make d cookies. Let us also assume that the total number of chips in the dough is λd . Now we will do something that may seem peculiar—or at least picky and obsessive. Pick out one chip from among all of them, and pick out one cookie from all those made. We want to analyze the probability that this one special designated chip is in this one special...
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This note was uploaded on 11/29/2011 for the course MATH 3355 taught by Professor Britt during the Spring '08 term at LSU.
- Spring '08