PMF for the sum of random variables

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Homework Help Overview

The discussion revolves around finding the probability mass function (PMF) for the sum of two independent uniform discrete random variables, specifically Z = X + Y, where X and Y take values between 1 and L or 1 and n. Participants are exploring the convolution method for determining the PMF.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • One participant mentions the use of convolution for the PMF and attempts to express it mathematically. Another suggests a geometric interpretation involving a grid of outcomes to visualize the problem. There are also indications of confusion regarding the correct application of known results.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some guidance has been offered regarding geometric visualization and the convolution method, but there is no explicit consensus on the correct approach or resolution of the confusion expressed by some participants.

Contextual Notes

There are mentions of different ranges for the random variables (1 to L and 1 to n), which may affect the interpretation of the problem. Additionally, there is a repeated emphasis on the need to apply known results correctly, suggesting that assumptions or definitions may be under scrutiny.

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

RGV
 
Ray Vickson said:
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
 
magnifik said:
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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