1 supposenbspu v wnbspare independent poisson random, Ask an Expert

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1. Suppose U; V; W are independent Poisson random variables with means ?; µ; r,, respectively. Let X D U C W; Y D V C W:

(a) Find the marginal pmfs of X and Y.

(b) Find the joint pmf of .X; Y /.

2. Suppose a fair die is rolled twice. Let X and Y be the two rolls. Find the following with as little calculation as possible:

(a) E.X C Y jY D y/.

(b) E.XY jY D y/.

(d) pX CY;X -Y :

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