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PMF for the sum of random variables

  1. Nov 8, 2011 #1
    For a sum of two independent uniform discrete random variables, Z = X + Y, what is the probability mass function of Z? X and Y both take on values between 1 and L

    I know that for the sum of independent rv's the PMF is a convolution
    so...
    Ʃ(1/k)(1/n-k) from k = 1 to L
    but i'm wondering.. can this be simplified?
     
  2. jcsd
  3. Nov 8, 2011 #2

    lanedance

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    these are good to do geometrically, consider the xy plane, we have LxL grid of discrete (X,Y) outcomes, each equi-probable, with probability 1/L^2

    Lines of constant Z=z have a slope of -x, and the probability of Z will be the number of discrete points intersected by a constant

    try drawing it, this should also help understand the analytic convolution method
     
  4. Nov 8, 2011 #3

    Ray Vickson

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    No wonder you are having trouble: you are 100% wrong in what you are writing. Go back and apply known results correctly.

    RGV
     
  5. Nov 8, 2011 #4
    For a sum of two independent uniform discrete random variables, Z = X + Y, what is the probability mass function of Z? X and Y both take on values between 1 and n

    I know that for the sum of independent rv's the PMF is a convolution
    so...
    Ʃ(1/k)(1/n-k) from k = 1 to n
     
  6. Nov 9, 2011 #5

    Ray Vickson

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    That is not the required convolution. I have no idea what it is.

    RGV
     
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