Real estate. A real-estate broker in Maastricht, the Netherlands, purchased 3 two-bedroom houses in a depressed market for a combined cost of €500,000. He expects the cleaning and repair costs for each house to average at €50,000 with a standard deviation of €5,000.

When he sells them, after subtracting taxes and other closing costs, he expects to realize an average of €225,000 per house with a standard deviation of €6,000.

a) Define your random variables. Use them to create a random variable for the broker’s net profit.

b) Find the mean (expected value) of the net profit.

c) Find the standard deviation of the net profit.

d) Do you have to assume independence for the repairs and sale prices of the houses? Explain.