Finding the joint probability of two random variables?

Questions
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1

Hi

I’m a newbie in Mathematica and I am currently practicing on utilizing the Probability functionalities. Attached is a notebook on a Joint Probability problem. I have worked out the answer manually but unfortunately its not the same as in Mathematica. I’m not sure where I have gone wrong in setting up the answer and I would appreciate any guidance that I can get.

Thanks in advance
Arasan

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2

Your problem description describes a parallelogram shaped region of uniform probability in the x y plane, but your implementation is for a rectangular region. I think you want

Probability[
  2 x + z == n, {x, z} \[Distributed] 
   ProductDistribution[DiscreteUniformDistribution[{-2, 4}], 
    DiscreteUniformDistribution[{-1, 1}]]];
DiscretePlot[%, {n, -6, 10}, ExtentSize -> 1/3]
3

Hi John, Many thanks for looking into this and reverting. This line matches the answer.

Have a good weekend.

Arasan