The joint probability mass function of two discrete random variables X and Y is

Question

https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=3300760520325458129

Answer 1

In the following µ represents lambda.

Marginal probability distributions are given by summations of the same function but different limits.

For x: P(X=x)=e^(-µ)∑((µ/2)^x)/(y!(x-y)!) with limits {low,high}={y=0,y=x} because x-y≥0 so that the factorial argument≥0. Example: if x=10, the limits are {0,10}.

For y: P(Y=y)=e^(-µ)∑((µ/2)^x)/(y!(x-y)!) with limits {x=y,x=∞}. Example: if y=10, the limits are {10,∞}.

I hope this answer helps.