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PMF for the sum of random variables

  • Thread starter magnifik
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  • #1
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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?
 

Answers and Replies

  • #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
 
  • #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
 
  • #4
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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
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
 
  • #5
Ray Vickson
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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
That is not the required convolution. I have no idea what it is.

RGV
 

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