:{e f(x, y) = [xe-0xy, > 0 0, otherwise Prove that: 1) marginal distribution fx(x) is...

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:{№²e f(x, y) = [x²e-0≤x≤y, λ> 0 0, otherwise Prove that: 1) marginal distribution fx(x) is exponential E (X) 2) conditional distribution f(y|x) is shifted exponential, f(y|x)= Xey-x), y ≥ x 3) conditional distribution f(y\x) is uniform U(0, y) Please solve 1, 2, and 3 please. :{№²e f(x, y) = [x²e-0≤x≤y, λ> 0 0, otherwise Prove that: 1) marginal distribution fx(x) is exponential E (X) 2) conditional distribution f(y|x) is shifted exponential, f(y|x)= Xey-x), y ≥ x 3) conditional distribution f(y\x) is uniform U(0, y) Please solve 1, 2, and 3 please.

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1 To find the joint distribution fy z we need to integrate the joint density fx y z over the variabl... View the full answer