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
