You have estimated the following probabilities for the returns of BHP and RIO in five different states of the economy: Economic State Probability BHP RIO Terrible 0.2 3% 3% Bad 0.2 4% 5% Average 0.2 5% 7% Good 0.2 6% 9% Great 0.2 7% 11% a) Calculate the mean and standard deviation of returns for the two firms. (4 marks) b) Plot both BHP and RIO on a chart where return is on the y-axis and standard deviation is on the x-axis. Using indifference curves, show on the graph the following three types of investors (3 marks) i) William is indifferent between BHP and RIO ii) Eugene prefers BHP to RIO iii) Merton prefers RIO to BHP c) Can all three investors be acting rationally? Discuss with reference to the risk and return of both BHP and RIO, and the critical assumption underlying mean-variance analysis