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The random variables X and Y have a joint density function given by f(x, y) =...

The random variables X and Y have a joint density function given by f(x, y) = ( 2e(−2x) /x, 0 ≤ x < ∞, 0 ≤ y ≤ x , otherwise.

(a) Compute Cov(X, Y ).

(b) Find E(Y | X).

(c) Compute Cov(X,E(Y | X)) and show that it is the same as Cov(X, Y ).

How general do you think is the identity that Cov(X,E(Y | X))=Cov(X, Y )?

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