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. 20 16 18 0.3 0.4 0.3 p(x) (a) Compute E(X), E(X2), and V(X). ft3 E(X)= E(X²)= V(x)= (b) If the price of a freezer having capacity X is 64X-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? (Enter your answer to four decimal places.) ft³

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