# Expected value of a sum.

1. Nov 1, 2013

### countzander

1. The problem statement, all variables and given/known data

Suppose that ∫X,Y(x,y) = λ2e-λ(x+y), 0 ≤ x, 0 ≤ y

Find E(X + Y)

2. Relevant equations

E(X + Y) = E(X) + E(Y)

3. The attempt at a solution

Since the expected vale of a sum is the sum of the expected values, I attempted to find the marginal pdfs of the joint pdf. But when calculating the integral for the marginal probability of X, pX(x) = ∫λ2e-λ(x+y) dy from 0 to ∞, the result is an undefined statement, division by zero.

2. Nov 1, 2013

### Ray Vickson

Remember that an integral from 0 to ∞ is a limit of the integral from 0 to U as U → ∞. Just do the integral from 0 to U first, then take the limit. Do it properly, and do it carefully.

3. Nov 1, 2013

### countzander

That's what I did. As I said in the original post, the limit is 0. But because the 0 appears in the denominator, the integral is undefined.

Does anyone know where the problem is?

4. Nov 1, 2013

### Staff: Mentor

I don't think so. Keep in mind that e-λ(x + y) = e-λx * e-λy, and that you are integrating with respect to y.

Also, both ex and e-x are positive for all real numbers x, so I think you might be confused about 0 appearing in the denominator.

5. Nov 1, 2013

### Ray Vickson

You need to show us your work, step-by-step. Otherwise, there is no way we can help you.

6. Nov 1, 2013

"Since the expected vale of a sum is the sum of the expected values, I attempted to find the marginal pdfs of the joint pdf. "

There is no need to do that.

7. Nov 1, 2013

### Ray Vickson

Agreed. But he ought to be ABLE to do it if he wants to pass the course.