Question: 5. (a) If F is a continuous distribution function, prove that F(x)F(dx) = 1 2 Thus show that if X1, X2 are iid with

5. (a) If F is a continuous distribution function, prove that F(x)F(dx) = 1 2 Thus show that if X1, X2 are iid with common distribution F, then 1 P[X1 X2] == //P 2 and E(F(X1)) = 1/2. (One solution method relies on Fubini's theo- rem.)

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