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Geometric and Hypergeometric Distributions 10/29

Introductory Probability:
Statistics 116

In this section we described the geometric distribution. We did this by looking at tossing a symmetric die that has proportion p of its faces painted white and q of its faces painted black where q = 1 - p and determining on which toss the first white face would appear. We looked at a tree diagram to distinguish between all the possibilities and came up with a general formula for the probability of success on the kth toss. We then looked at some examples including the Craps principle.


Next we described the hypergeometric distribution. We did this by considering N elements of which G were ``good'' and B were ``bad'', then considered the number of ways we could choose g ``good'' and b ``bad'' from those G ``good'' and B ``bad''. We compared the hypergeometric distribution (sampling without replacement) to the binomial (sampling with replacement) and saw how if N was very large there would be no difference between the two distributions. Finally we looked at a simple example to illustrate use of the hypergeometric distribution.


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Susan Holmes
1998-12-07