Question

Expense Forecasts: The budgeting process for a mid-western college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: .3, .2, .25, .05, and .2.

a. Show the probability distributions for the expense forecast.

b. What is the expected value of the expense forecast for the coming ear?

c. What is the variance of the expense forecast for the coming year.

d. If income projections for the ear are estimated at $12 million, comment on the financial position of the college.

Answer 1

a) probability distributions for the expense forecast is as follows:

x	P(x)
9	0.30
10	0.20
11	0.25
12	0.05
13	0.20

b)

from above:

x	f(x)	xP(x)	x2P(x)
9	0.30	2.7000	24.3000
10	0.20	2.0000	20.0000
11	0.25	2.7500	30.2500
12	0.05	0.6000	7.2000
13	0.20	2.6000	33.8000
	total	10.6500	115.5500
	E(x) =μ=	ΣxP(x) =	10.6500
	E(x2) =	Σx2P(x) =	115.5500
	Var(x)=σ2 =	E(x2)-(E(x))2=	2.1275

  expected value of the expense forecast for the coming ear =10.65

c)

variance of the expense forecast for the coming year =2.1275

d)

since the income projections are higher than expense forecast ,  college appears to be profitable in coming year