An certain brand of upright freezer is available in three different rated capaci

Question

An certain brand of upright freezer is available in three different rated capacities: 16 ft^3, 18 ft^3, and 20 ft^3. Let x = the rated capacity of a freezer of this brand sold at store. Suppose that X has the following pmf. (a) Compute E(X), E(x^2), and v(x). E(x) = ft^3 E(x^2) = v(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? (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- 0.009x^2. what is the expected actual capacity of the freezer purchase by the next customer?

Explanation / Answer

x

16

18

20

P(x)

0.4

0.3

0.3

E(x) = x*P(x) = 16*0.4+18*0.3+20*0.3 = 17.8 ft3

E(x2) = x2*P(x) = 162*0.4+182*0.3+202*0.3 = 319.6

V(x) = E(x2) – E(x)2 = 319.6 – 17.82 = 2.76

E(60x – 650) = 60*E(x) – 650 = 60*17.8 – 650 = $418

V(60x – 650) = 602*V(x) = 602*2.76 = 9936

E(x – 0.009x2) = E(x) – 0.009*E(x2) = 17.8 – 0.009*319.6 = 14.9236 ft3

x

16

18

20

P(x)

0.4

0.3

0.3

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