Question

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 $Y_1$ denote the number of married executives and $Y_2$ denote the number of never-married executives among the three selected for promotion. Assume that the three are randomly selected from the nine available. We determined that the joint probability distribution of $Y_1$ and $Y_2$ is given by $$p(y_1, y_2) = \frac{{4 \choose y_1}{3 \choose y_2}{2 \choose 3 - y_1 - y_2}}{{9 \choose 3}}$$ where $y_1$ and $y_2$ are integers, $0 \le y_1 \le 3$, $0 \le y_2 \le 3$, and $1 \le y_1 + y_2 \le 3$. We also determined that the marginal probability distribution of $Y_1$ is a hypergeometric distribution with $N = 9$, $n = 3$, and $r = 4$. Find the expected number of married executives among the three selected for promotion. married executives

          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 $Y_1$ denote the number of married executives and $Y_2$ denote the number of never-married executives among the three selected for promotion. Assume that the three are randomly selected from the nine available.
We determined that the joint probability distribution of $Y_1$ and $Y_2$ is given by
$$p(y_1, y_2) = \frac{{4 \choose y_1}{3 \choose y_2}{2 \choose 3 - y_1 - y_2}}{{9 \choose 3}}$$
where $y_1$ and $y_2$ are integers, $0 \le y_1 \le 3$, $0 \le y_2 \le 3$, and $1 \le y_1 + y_2 \le 3$. We also determined that the marginal probability distribution of $Y_1$ is a hypergeometric distribution with $N = 9$, $n = 3$, and $r = 4$. Find the expected number of married executives among the three selected for promotion.
married executives

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. Assume that the three are randomly selected from the nine available.
We determined that the joint probability distribution of Y1 and Y2 is given by

p(y1, y2) = (4 y13 y22 3 - y1 - y2)/(9 3)

where y1 and y2 are integers, 0 ≤ y1 ≤ 3, 0 ≤ y2 ≤ 3, and 1 ≤ y1 + y2 ≤ 3. We also determined that the marginal probability distribution of Y1 is a hypergeometric distribution with N = 9, n = 3, and r = 4. Find the expected number of married executives among the three selected for promotion.
married executives

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