2.11 Isabella just inherited a small hotel in a seaside town from her aunt. In good years (those without rain and with plenty of sunshine), she earns $200,000 from the hotel. If the weather is poor, demand for the hotel drops and she loses $50,000. Isabella’s estimate of the probability of good weather is 75%.

a. Calculate the expected value and the variance of Isabella’s income from the hotel.

b. Isabella is risk averse. Sun and Fun, a hotel chain, offers Isabella a guaranteed payment of

$145,000 each year in exchange for the position of manager of the hotel (Sun and Fun would get all the earnings from the hotel). Will she accept this offer? Explain.

c. Why might Sun and Fun make such an offer?