Catalina just inherited a vineyard from a distant relative. In good years (when there is no rain or frost during harvest season), she earns $ 100,000 from the sale of grapes from the vineyard. If the weather is poor, she loses $ 20,000. Catalilna’s estimate of the probability of good weather is 60%.

a. Calculate the expected value and the variance of Catalina’s income from the vineyard.

b. Catalina is risk averse. Ethan, a grape buyer, offers Catalina a guaranteed payment of $ 70,000 each year in exchange for her entire harvest. Will she accept this offer? Explain.

c. Why might Ethan make such an offer?