Concept explainers
In Exercise 5.3, we determined that the joint probability distribution of Y1, the number of married executives, and Y2, the number of never-married executives, is given by
where y1 and y2 are integers. 0 ≤ y1 ≤ 3, 0 ≤ y2 ≤ 3, and 1 ≤ y1 + y2 ≤ 3. Are Y1 and Y2 independent? (Recall your answer to Exercise 5.21.)
5.3 Of nine executives in a business firm, four are married, three have never married, and two are divorced. Three of the executives are to be selected for promotion. Let Y1 denote the number of married executives and Y2 denote the number of never-married executives among the three selected for promotion. Assuming that the three are randomly selected from the nine available, find the joint probability
5.21. In Exercise 5.3, we determined that the joint probability distribution of Y1, the number of married executives, and Y2, the number of never-married executives, is given by
where y1 and y2 are integers. 0 ≤ y1 ≤ 3, 0 ≤ y2 ≤ 3, and 1 ≤ y1 + y2 ≤ 3.
- a Find the marginal probability distribution of Y1, the number of married executives among the three selected for promotion.
- b Find P(Y1 = 1|Y2 = 2).
- c If we let Y3 denote the number of divorced executives among the three selected for promotion, then Y3 = 3 – Y1 – Y2. Find P(Y3 = 1|Y2 = 1).
- d Compare the marginal distribution derived in (a) with the hypergeometric distributions with N = 9, n = 3, and r = 4 encountered in Section 3.7.
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Mathematical Statistics with Applications
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