29. The yield/acre of wheat on a given parcel of land can be represented as the outcome of a random variable Y defined by Y ¼ 10x1/3ee for x∈[8,100], where Y ¼ wheat output in bushes/acre x ¼ pounds/acre of fertilizer applied e ¼ is a random variable having the probability density function fð Þ¼ e 3e3e Ið Þ 0;1 ð Þe .

(a) If fertilizer is applied at the rate of 27 lb/acre, what is the probability that greater than 50 bushels/acre of wheat will be produced?

(b) You sign a forward contract to sell your wheat for

$3.00/bushel at harvest time. Fertilizer costs $0.20/

lb. If you apply fertilizer at a rate of 27 lb/acre, what is your expected return above fertilizer cost, per acre?

(c) What is the variance of Y if fertilizer is applied at the rate of 27 lb/acre? Does the variance of Y change if a different level of fertilizer is applied? Why or why not?