February 2019
Intermediate to advanced
634 pages
17h 41m
English
Content preview from Introduction to Probability, Second Edition, 2nd Edition
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3.9 Connections between Binomial and Hypergeometric
The Binomial and Hypergeometric distributions are connected in two important ways. As we will see in this section, we can get from the Binomial to the Hypergeometric by conditioning, and we can get from the Hypergeometric to the Binomial by taking a limit. We’ll start with a motivating example.
Example 3.9.1 (Fisher exact test). A scientist wishes to study whether women or men are more likely to have a certain disease, or whether they are equally likely. A random sample of n women and m men is gathered, and each person is tested for the disease (assume for this problem that the test is completely accurate). The numbers of women and men in the sample who have the disease are X and Y respectively, ...
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