Question: (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 2 ).

(i) Let X be a random variable taking on the values – 1 and 1, each with probability 1/2. Find E(X) and E(X2).

(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[g(X)] + g[E(X)]

Can you conclude that E1F2 5 1?

E[g(X)] + g[E(X)]

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