Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0. elsewhere (a) Find the...

Let X1 and X2 have the joint pdf

f(x1,x2) = 2 0<x1<x2<1; 0. elsewhere
(a) Find the conditional densities (pdf) of X1|X2 = x2 and X2|X1 = x1.
(b) Find the conditional expectation and variance of X1|X2 = x2 and X2|X1 = x1.
(c) Compare the probabilities P(0 < X1 < 1/2|X2 = 3/4) and P(0 < X1 < 1/2).
(d) Suppose that Y = E(X2|X1). Verify that E(Y ) = E(X2), and that var(Y ) ≤ var(X2).

Expert Solution

orchestra answered 1 year ago

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