Suppose that the conditional distribution of Y given X = x is Poisson with mean E(Y|x) = x, and that X ~ exp(1)

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Could you solve (d),(e),(f)?

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Suppose that the conditional distribution of Y given X = x is Poisson with mean A =
E(Y|x) = x, and that X ~ exp(1)
(a) Find fy (y)
(b) Find E(Y)
(c) Find Var(Y)
(d) Find Var(E(Y|X)
(e) Find E(Var(Y|X))
(f) Find f(x|y)
(g) Find E(X|Y)
(h) Find E(E(X|Y)) without using iterative expectation formula.
Transcribed Image Text:Suppose that the conditional distribution of Y given X = x is Poisson with mean A = E(Y|x) = x, and that X ~ exp(1) (a) Find fy (y) (b) Find E(Y) (c) Find Var(Y) (d) Find Var(E(Y|X) (e) Find E(Var(Y|X)) (f) Find f(x|y) (g) Find E(X|Y) (h) Find E(E(X|Y)) without using iterative expectation formula.
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