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Expected value of a sum.

  1. Nov 1, 2013 #1
    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. jcsd
  3. Nov 1, 2013 #2

    Ray Vickson

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    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.
     
  4. Nov 1, 2013 #3
    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?
     
  5. Nov 1, 2013 #4

    Mark44

    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.
     
  6. Nov 1, 2013 #5

    Ray Vickson

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    You need to show us your work, step-by-step. Otherwise, there is no way we can help you.
     
  7. Nov 1, 2013 #6

    statdad

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    "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.
     
  8. Nov 1, 2013 #7

    Ray Vickson

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