An certain brand of upright freezer is available in three different rated capacities: 16 fts, 18 fts, and 20 ft. Let X = the rated

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An certain brand of upright freezer is available in three different rated capacities: 16 fts, 18 fts, and 20 ft. 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 ) 0.3 0.2 0.5 (a) Compute E(X ), E(X2), and V(X). E(X) = ft 3 E ( X 2 ) = V ( X ) = (b) If the price of a freezer having capacity X is 61X - 650, what is the expected price paid by the next customer to buy a freezer? (c) What is the variance of the price paid by the next customer? (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? ft 3