This problem introduces a variation on the Monte Carlo integration technique of Example A of Section 5.2. Suppose that we wish to evaluate b I(f)=/ f(x)dx Let g be a density function on [a, 1)]. Generate X 1, I by - - - , X" from g and estimate a. Show that E(I(f)) = I(f). b. Find an expression for Var(I(f)). Give an example for which it is finite and an example for which it is infinite. Note that if it is finite, the law of large numbers implies that I (f) -> I(f) as n -> . c. Show that if a = 0, b = 1, and g is uniform, this is the same Monte Carlo estimate as that of Example A of Section 5.2. Can this estimate be improved by choosing g to be other than uniform? (Hint: Compare variances.)