To solve this problem, we are asked to calculate $E(X + Y)$, where:

• $X$ is the random variable representing the number of men in the interview pool.
• $Y$ is the random variable representing the number of women in the interview pool.

The key observation here is that $X + Y$ represents the total number of people selected for the interview, which will always be 2, since exactly 2 applicants are chosen.

Calculation:

Let’s break this down:

1. Total number of applicants: There are 6 men and 5 women, giving us a total of: $6 + 5 = 11 \text{ applicants}.$

2. Random variables $X$ and $Y$:

   • $X$ denotes the number of men selected.
   • $Y$ denotes the number of women selected. The relationship between these variables is straightforward: $X + Y = 2.$

3. Expected value $E(X + Y)$: Since $X + Y$ is always 2 (i.e., the number of selected applicants), the expected value of $X + Y$ is simply: $E(X + Y) = 2.$

Thus, the value of $E(X + Y)$ is $2$.

Summary:

The expected value of $X + Y$, which represents the total number of people selected for the interview, is $\mathbf{2}$.

Would you like any additional details on this problem? Here are some related questions for further practice:

1. What is the expected number of men selected for the interview?
2. What is the expected number of women selected for the interview?
3. What is the probability that both applicants selected are men?
4. What is the probability that both applicants selected are women?
5. What is the probability that one man and one woman are selected?

Tip: When dealing with expected values, always consider the inherent constraints of the situation, as they can simplify your calculations significantly.