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X and Y are independent, each U(0,1). Define W = min(X, Y) and V = max(X, Y) as the smaller and larger of these variables.

X and Y are independent, each U(0,1). Define W = min(X, Y) and V = max(X, Y) as the smaller and larger of these variables. Find the densities of V, W; are they independent? Show that E(VW) = 1/4.

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