Gavin Jones's friend is planning to invest $1 million in a rock concert to be held 1 year from now. The friend figures that he will obtain $4 million revenue from his $1 million investment - unless, my goodness, it rains. If it rains, he will lose his entire investment. There is a 25% 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 $0.55, and this unit pays $1 if it rains and nothing if it does not. He may purchase as many units as he wishes, up to $4 million. (i) What is the expected rate of return on his investment if he buys y million units of insurance? (The cost of insurance is addition to his $1 million investment.) [10 marks) (ii) What number of units will minimize the variance of his return? What is this mini- mum value? And what is the corresponding expected rate of return? [10 marks)