(i) Let X be a random variable taking on the values – 1 and 1, each with probability 1/2. Find E(X) and E(X'). (ii) Now let X be a random variable taking on the values 1 and 2, each with probability 1/2. Find E(X) and E(1/X). (iii) Conclude from parts (i) and (ii) that, in general, E[g(X)] + g[E(X)] for a nonlinear function g(-). (iv) Given the definition of the F random variable in equation (B.43), show that E(F) = E [(X/k2). Can you conclude that E(F) = 1?

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