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One Function of Two Random Variables

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data

    f(x,y) = x + y 0≤x≤1, 0≤y≤1
    zero , otherwise

    Show that X+Y has density f(z) = z^2, 0 < z < 1, and z(2-z), 1 < z < 2.

    2. Relevant equations
    Also, how to find the density f(z) for X*Y?

    3. The attempt at a solution
    Even if f(z) is not given, some questions asks to find f(z) like what I wrote in the relevant question. My problem is how to find the limits of the integration, and how I know that I would have 0 < z < 1, and 1 < z < 2. I'm struggling with this problem since last week, and I really need your help.
  2. jcsd
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