You manage a rental property. The likelihood of a vacancy in any given month is 12%. The monthly mortgage payment on the property is $2000. You estimate that the maintenance cost every month is given by a normal distribution with a mean of $100 and a standard deviation of $50. Additional administrative expenses are given by a uniform distribution between $0 and $100. Finally, the monthly rental income when the property is occupied is $3500. Assume that all of the costs (mortgage, maintenance, and administrative) are incurred even if the property is vacant. Also, you do not need to discount the cash flows in answering this question.

a. What is the average monthly cash flow? (10 points)

b. What is the probability that your monthly cash flow is between $1000 and $2000? (5 points)

c. Suppose your mortgage payments are higher. Specifically, the additional mortgage cost is given by a uniform distribution between $0 and $50. What is your annual average cash flow and standard deviation?