The budgeting process for a midwestern college resulted in expense forecasts for

Question

The budgeting process for a midwestern 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: 0.29, 0.18, 0.25, 0.1, and 0.18. a. Show the probability distribution for the expense forecast. b. What is the expected value of the expense forecast for the coming year (to 2 decimals)? c. What is the variance of the expense forecast for the coming year (to 2 decimals)? d. If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)?

Explanation / Answer

a) The probability density is already given and is filled as:

b) The expected forecast for the coming year is computed as:

E(X) = 9*0.29 + 10*0.18 + 11*0.25 + 12*0.1 + 13*0.18 = 10.7

Therefore the expected forecasted value is 10.7

c) The variance if the expected value is computed as:

Var(X) = E(X2) - (E(X))2

E(X2) = 92*0.29 + 102*0.18 + 112*0.25 + 122*0.1 + 132*0.18 = 116.56

Therefore, variance is now computed as:

Var(X) = E(X2) - (E(X))2= 116.56 - 10.72 = 2.07

Therefore the variance is 2.07

d) Expected profit = estimated income - expected expense = 12 - 10.7 = 1.3

Therefore expected profit would be $1.30 million

X f(x) 9 0.29 10 0.18 11 0.25 12 0.1 13 0.18

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