You are interested in buying a stock that has a price of $42. You have projected that next year there is: a 10% probability the stock will equal $1, a 20% probability the stock will equal $31, a 30% probability the stock will equal $43, a 30% probability the stock will equal $55, and a 10% probability the stock will equal $80. Answer the following (showing all work):
(a) what is the expected return on the stock if you buy today and sell next year?
(b) what is the expected standard deviation of the stock?