14. -6 points DevoreStat9 3.E.032 My Notes Ask Your An certain brand of upright

Question

14. -6 points DevoreStat9 3.E.032 My Notes Ask Your An certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 t3, 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 16 18 20 p(x) 0.2 0.5 0.3 (a)Compute E(), Ex, and vo ft3 E(X) E(x2)- (b) If the price of a freezer having capacity X is 65x - 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 - 0.008x2. What is the expected actual capacity of the freezer purchased by the next customer? ft3

Explanation / Answer

14)

E(X) =18.2

E(X2) =333.2

V(X) = E(X2) -(E(X))2 =1.96

b)

expected price =65E(X)-650 =65*18.2-650=533

c)

variance =652Var(X) =8281

d)

E(h(x) =E(X)-0.008E(X2) =15.5344

x P(x) xP(x) x^2P(x) 16 0.2 3.2 51.2 18 0.5 9 162 20 0.3 6 120 total 18.2 333.2

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