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Suppose that Y1 and Y2 are independent binomial
Chapter 5, Problem 40E(choose chapter or problem)
Problem 40E
Suppose that Y1 and Y2 are independent binomial distributed random variables based on samples of sizes n1 and n2, respectively. Suppose that p1 = p2 = p. That is, the probability of “success” is the same for the two random variables. Let W = Y1 + Y2. In Chapter 6 you will prove that W has a binomial distribution with success probability p and sample size n1 + n2. Use this result to show that the conditional distribution of Y1, given that W = w, is a hypergeometric distribution with N = n1 + n2, n = w, and r = n1.
Questions & Answers
QUESTION:
Problem 40E
Suppose that Y1 and Y2 are independent binomial distributed random variables based on samples of sizes n1 and n2, respectively. Suppose that p1 = p2 = p. That is, the probability of “success” is the same for the two random variables. Let W = Y1 + Y2. In Chapter 6 you will prove that W has a binomial distribution with success probability p and sample size n1 + n2. Use this result to show that the conditional distribution of Y1, given that W = w, is a hypergeometric distribution with N = n1 + n2, n = w, and r = n1.
ANSWER:
Solution
Step 1 of 1
We have to prove that W is binomial distribution with probability p and sample size n1+n2
Given that conditional distribution of Y1 given w is a hypergeometric distribution with N=n1+n2,
Let Y1 and Y2 are two binomial distributed random variables with sample sizes n1 and n2