nci types of service providers. 61. The budgeting process for a midwestern colle

Question

nci types of service providers. 61. The budgeting process for a midwestern college resulted in expense forecasts for the com- ing year (in S 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 distribution for the expense forecast. b. What is the expected value of the expense forecast for the coming year? c. What is the variance of the expense forecast for the coming year? d. If income projecti ons for the year are estimated at $12 million, comment on the financial position of the college

Explanation / Answer

a) Sum of all probability = 0.3 + 0.2 + 0.25 + 0.05 + 0.2 = 1

Since sum is equal to 1, this is a probability distribution

b) E(X) = 9 * 0.3 + 10 * 0.2 + 11 * 0.25 + 12 * 0.05 + 13 * 0.2 = 10.65

c) E(X2) = 92 * 0.3 + 102 * 0.2 + 112 * 0.25 + 122 * 0.05 + 132 * 0.2 = 115.55

Var(X) = E(X2) - (E(X))2 = 115.55 - 10.652 = 2.1275

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