a. Explanation Calculation: It is given that, Urn contains p black balls, q white balls and r red balls; and n balls are chosen without replacement. The hypergeometric distribution for two categories (success and failure) is p ( y ) = ( r n ) ( N − r n − y ) ( N n ) Generalize the hypergeometric distribution for three categories is, p ( x , y ) = ( p x ) ( q y ) ( N − p − q n − x − y ) ( N n ) Define the variable: x : number of black balls y : number of white balls z : number of red balls Here, the population size is N = p + q + r . Let n be number of draws, r 1 = p , r 2 = q , r 3 = r and z = n − x − y Therefore, p ( x , y , z ) = ( p x ) ( q y ) ( ( p + q + r ) − p − q n b. To determine Find the joint distribution of the numbers of black and white balls in the sample. c. To determine Find the marginal distribution of the numbers of white balls in the sample.

Mathematical Statistics and Data Analysis

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Author: John A. Rice

Publisher: Cengage Learning

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Chapter 3.8, Problem 2P

To determine

Find the joint distribution of the numbers of black, white, and red balls in the sample.

To determine

Find the joint distribution of the numbers of black and white balls in the sample.

To determine

Find the marginal distribution of the numbers of white balls in the sample.

Expert Solution & Answer

Chapter 3 Solutions

Mathematical Statistics and Data Analysis

Ch. 3.8 - Prob. 1P Ch. 3.8 - Prob. 2P Ch. 3.8 - Prob. 3P Ch. 3.8 - Prob. 4P Ch. 3.8 - Prob. 5P Ch. 3.8 - Prob. 6P Ch. 3.8 - Prob. 7P Ch. 3.8 - Prob. 8P Ch. 3.8 - Prob. 9P Ch. 3.8 - Prob. 10P

Ch. 3.8 - Prob. 11P Ch. 3.8 - Prob. 12P Ch. 3.8 - Prob. 13P Ch. 3.8 - Prob. 14P Ch. 3.8 - Prob. 15P Ch. 3.8 - Prob. 16P Ch. 3.8 - Prob. 17P Ch. 3.8 - Prob. 18P Ch. 3.8 - Prob. 19P Ch. 3.8 - Prob. 20P Ch. 3.8 - Prob. 22P Ch. 3.8 - Prob. 23P Ch. 3.8 - Prob. 24P Ch. 3.8 - Prob. 25P Ch. 3.8 - Prob. 27P Ch. 3.8 - Prob. 28P Ch. 3.8 - Prob. 29P Ch. 3.8 - Prob. 30P Ch. 3.8 - Prob. 31P Ch. 3.8 - Prob. 32P Ch. 3.8 - Prob. 33P Ch. 3.8 - Prob. 34P Ch. 3.8 - Prob. 35P Ch. 3.8 - Prob. 38P Ch. 3.8 - Prob. 39P Ch. 3.8 - Prob. 44P Ch. 3.8 - Prob. 45P Ch. 3.8 - Prob. 46P Ch. 3.8 - Prob. 47P Ch. 3.8 - Prob. 48P Ch. 3.8 - Prob. 50P Ch. 3.8 - Prob. 51P Ch. 3.8 - Prob. 52P Ch. 3.8 - Prob. 53P Ch. 3.8 - Prob. 54P Ch. 3.8 - Prob. 55P Ch. 3.8 - Prob. 56P Ch. 3.8 - Prob. 57P Ch. 3.8 - Prob. 58P Ch. 3.8 - Prob. 60P Ch. 3.8 - Prob. 61P Ch. 3.8 - Prob. 62P Ch. 3.8 - Prob. 63P Ch. 3.8 - Prob. 64P Ch. 3.8 - Prob. 65P Ch. 3.8 - Prob. 66P Ch. 3.8 - Prob. 67P Ch. 3.8 - Prob. 68P Ch. 3.8 - Prob. 69P Ch. 3.8 - Prob. 70P Ch. 3.8 - Prob. 71P Ch. 3.8 - Prob. 72P Ch. 3.8 - Prob. 73P Ch. 3.8 - Prob. 74P Ch. 3.8 - Prob. 75P Ch. 3.8 - Prob. 76P Ch. 3.8 - Prob. 77P Ch. 3.8 - Prob. 78P Ch. 3.8 - Prob. 79P Ch. 3.8 - Prob. 80P Ch. 3.8 - Prob. 81P

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