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STAT 120 Suppose that X have a gamma distribution with parameters a = 2 and θ=...

STAT 120 Suppose that X have a gamma distribution with parameters a = 2 and θ= 3, and suppose that the conditional distribution of Y given X=x, is uniform between 0 and x.

(1) Find E(Y) and Var(Y).

(2) Find the Moment Generating Function (MGF) of Y. What is the distribution of Y?

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