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In: Statistics and Probability

Let X and Y be random variables such that Y|X ∼ Gamma(3,1/X) X ∼ Gamma(3,3). (d)...

Let X and Y be random variables such that Y|X ∼ Gamma(3,1/X) X ∼ Gamma(3,3).

(d) Find EY . Hint: Use iterated expectation.

(e) Find E(1/X2).

(f) Find VarY .

(g) Find Cov(X,Y ).

(h) Find corr(X,Y ).

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