(Solved): An certain brand of upright freezer is available in three different rated capacities: 16 ft, 18 ...

An certain brand of upright freezer is available in three different rated capacities: 16 ft³, 18 ft3, and 20 ft³. Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose that X has the following pmf. X 16 18 20 p(x) 0.4 0.1 0.5 (a) Compute E(X), E(X2), and V(X). E(X) = 17.2 X ft³ E(X2) = 297.6 X V(X) = 1.76 X (b) If the price of a freezer having capacity X is 60X- 650, what is the expected price paid by the next customer to buy a freezer? $ 536.8 X (c) What is the variance of the price paid by the next customer? 8379.36 X (d) Suppose that although the rated capacity of a freezer is X, the actual capacity is h(X) = X-0.009x². What is the expected actual capacity of the freezer purchased by the next customer? (Enter your answer to four decimal places.) 14.8192 X ft³