Question

PROBLEM 9.1 (pg 113, #32) An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage space, respectively. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pdf: *(X 0.2 a. Compute E[X] 0.1 0.7 (which is alternatively expressed as Mx) b. Compute E[X²] (alternatively expressed as x?) C. Compute Var[X] (alternatively expressed as d. If the price of a freezer having capacity X is 20% -8, what is the expected price to be paid by the next customer or E[20X - 8]. e. What is the variance of the price 20X - 8 paid by the next customer or Var[20X-8].

please explain and show work for my understanding.

Answer 1

x	f(x)	xP(x)	x2P(x)
13.5	0.1000	1.3500	18.2250
15.9	0.7000	11.1300	176.9670
19.1	0.2000	3.8200	72.9620
	total	16.300	268.1540
	E(x) =μ=	ΣxP(x) =	16.3000
	E(x2) =	Σx2P(x) =	268.1540
	Var(x)=σ2 =	E(x2)-(E(x))2=	2.4640

from above

a)

E(X) =16.30

b)

E(X²) =268.1540

c)

σ² =2.4640

d)

expected price =20*E(X)-8=20*16.30-8 =318

e)

Var(20X-8)=20²*Var(X)=400*2.464 =985.6