Question

In: Math

The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in...

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, 0.17, 0.25, 0.07, and 0.22.

  1. Show the probability distribution for the expense forecast.
    x f(x)
    9
    10
    11
    12
    13

  2. What is the expected value of the expense forecast for the coming year (to 2 decimals)?

  3. What is the variance of the expense forecast for the coming year (to 2 decimals)?

  4. 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)?

Solutions

Expert Solution

a) The probability of expense being $9 millions is 0.29, $10 is 0.17, $11 is 0.25, $12 is 0.07 and $13 is 0.22.

Hence the  probability distribution for the expense forecast is

x f(x)
9 0.29
10 0.17
11 0.25
12 0.07
13 0.22

b) the expected value of X is

ans: the expected value of the expense forecast for the coming year is $10.76 millions

c) The variance of X is calculated as

First the expectation of

Now the variance is

ans: the variance of the expense forecast for the coming year is 2.22

c) The profit is

where Expense is the variable X in part a)

The expected value of Profit is

ans: If income projections for the year are estimated at $12 million, the college expect to make a profit of $1.24 millions


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