Question

An industrial firm needs to buy new computers by the end of the year. The exact number of the computers depends on the frequency of repair of the units observed the previous year. Assume that the number of computers bought per year X has the probability distribution as reported in the table below. Consider that the cost for each newly purchased unit is $1500, and by the end of the year company will receive a refund of 50X² dollars.

x	0	1	2	3
f(x)	3/10	3/10	1/5	1/5

1. How many computers the company is expected to purchase for the next year?

1. 13/10               b)   2                c)   17/10                d) 1         

2. How much money the company is expected to spend this year?

1. $1,865.5                      b)   $2,405.5                c)   $2,365              d) $1,805

3. How much money the company is expected to spend this year if the refund is denied?

1. $2,550             b)   $2,405.5                c)   $1,950              d) $2,800

Answer 1

a)

x	P(X=x)	xP(x)	x2P(x)
0	3/10	0.00000	0.00000
1	3/10	0.30000	0.30000
2	1/5	0.40000	0.80000
3	1/5	0.60000	1.80000
total		1.3000	2.9000
	E(x) =μ=	ΣxP(x) =	1.3000
	E(x2) =	Σx2P(x) =	2.9000

expected to purchase =E(x) =13/10

b)

expected to spend =E(1500X-50X²)=1500*13/10-50*2.9 =1805

c)

expected to spend this year if the refund is denied =E(1500X) =1500*13/10=1950