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A committee of three people is to be randomly selected
Chapter 5, Problem 148SE(choose chapter or problem)
Problem 148SE
A committee of three people is to be randomly selected from a group containing four Republicans, three Democrats, and two independents. Let Y1 and Y2 denote numbers of Republicans and Democrats, respectively, on the committee.
a What is the joint probability distribution for Y1 and Y2?
b Find the marginal distributions of Y1 and Y2.
c Find P(Y1 = 1|Y2 ≥ 1).
Questions & Answers
QUESTION:
Problem 148SE
A committee of three people is to be randomly selected from a group containing four Republicans, three Democrats, and two independents. Let Y1 and Y2 denote numbers of Republicans and Democrats, respectively, on the committee.
a What is the joint probability distribution for Y1 and Y2?
b Find the marginal distributions of Y1 and Y2.
c Find P(Y1 = 1|Y2 ≥ 1).
ANSWER:
Solution
Step 1 of 3
a) We have to find joint probability distribution function of
Here the committee is forming with 3 people
Let represents the number of republicans
Let represents the number of democrats
represents the number of independents
There 4 republicans 3 democrats and 2 independents
So there 9 people
Here are discrete random variables
Because are finite sample from finite population
So the distribution is hypergeometric distribution
Hence