Solution Found!
Consider the following method for creating a bivariate Poisson (a joint distribution for
Chapter 7, Problem 55(choose chapter or problem)
Consider the following method for creating a bivariate Poisson (a joint distribution for two r.v.s such that both marginals are Poissons). Let X = V + W, Y = V + Z where V, W, Z are i.i.d. Pois() (the idea is to have something borrowed and something new but not something old or something blue). (a) Find Cov(X, Y ). (b) Are X and Y independent? Are they conditionally independent given V ? (c) Find the joint PMF of X, Y (as a sum).
Questions & Answers
QUESTION:
Consider the following method for creating a bivariate Poisson (a joint distribution for two r.v.s such that both marginals are Poissons). Let X = V + W, Y = V + Z where V, W, Z are i.i.d. Pois() (the idea is to have something borrowed and something new but not something old or something blue). (a) Find Cov(X, Y ). (b) Are X and Y independent? Are they conditionally independent given V ? (c) Find the joint PMF of X, Y (as a sum).
ANSWER:Step 1 of 4
Given:
The variables are X = V + W, Y = V + Z where V, W, Z are i.i.d. Pois().