5. (Rain insurance) Gavin Jones's friend is planning to invest SI million in a rock concert to be held 1 year from now. The friend figures that he will obtain $3 million revenue from his $1 million investment-unless, my goodness, rains If it rains, he will lose his entire investment There is a 50% chance that it will rain the day of the concert Gavin suggests that he buy rain insurance He can buy one unit of insurance for $.50, and this unit pays S1 if t rains and nothing if it does not He may purchase as many units as he wishes, up to $3 million (a) What is the expected rate of return on his investment if he buys units of insurance? (The cost of insurance is in addition to his $1 million investment) (b) What number of units will minimize the variance of his return? What is this minimunm value? And what is the corresponding expected rate of return[Hint Before calculating a general expression for variance, think about a simple answer ]