Question

1. (Sec. 3.3, 32) A certain brand of upright freezer is available in four different rated capacities: 16ft", 18ft", 20fts and 22ft. Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose that X has pmf: 2 16 pxa) | 0.2 18 0.4 20 0.3 22 0.1 (a) Compute E[X], E[X2], and Var[X]. (b) If the price of a freezer having capacity X is given by Y = 70X-650, what is the expected price paid by the next customer to buy a freezer? Le. what is E[Y]? (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 given by W = X – 0.007X? What is the expected actual capacity of the freezer purchased by the next customer?

Answer 1

ANGWER a) F(x) = &c. P(x) = 16(0.2) +18 (0.4)+ 2060.3 +22 (0:1) E =18.6 E (x2) = Exo Po -609 (02) +(18)2 (0:4) +(90)) (6-3) +(22) (01) E(+2) = 349.2 VG) = f(x2) - [E G)]? = 349.9 –(8.632 V(x) = 3.94 D E 17031-650] - E (108-650) P6x) =470)(a) +1610) (0-4) +(150)(0:3) +(890) (0-1) = 652 C) E (701-650)] - E (70X-65052 PGV) - (47032 (0.9) 7(61039 (0:4) +(15032 (03) +(8401200 2440980 V( 70X-650) - E (108-6500 - [6 (70X- 650)|* = 440980-(652) -- 15876 d with Carner

d) E (X-0.007se) = Ebe) -0.0078(22) = 18.6-0.007(3492) = 18.6-2.4444 = 16.1556 Scanned with CamScanner