Question

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.

x	16	18	20
p(x)	0.4	0.3	0.3

(a) Compute E(X), E(X²), and V(X).

E(X)	=  ft3
E(X2)	=
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 − 0.009X². What is the expected actual capacity of the freezer purchased by the next customer?

Answer 1

All the answers are highlighted in red.

16	0.4	6.4	256	102.4
18	0.3	5.4	324	97.2
20	0.3	6	400	120

-----------------------------------------------------------------------------

-----------------------------------------------------------------------------

-----------------------------------------------------------------------------