An certain brand of upright freezer is available in three different rated capacities: 16 ft, 18 ft, 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. 16 18 20 p(x) 0.5 0.3 0.2 (a) Compute E(X), E(X²), and V(X). E(X) = 17.5 E(X2) = 305.2 V(X) = 2.44 v ft3 (b) If the price of a freezer having capacity X is 62X - 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?

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If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

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The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.