Read the writings and answer the following questions.

A life insurance company sells a last survivor annuity of $500 pa to a man aged 65 and a woman aged 70. The single premium for the policy is $8,500. The benefit is paid annually in advance. (i) Assuming that expenses can be ignored, write down a random variable that represents the present value of the profit made on one of these policies, as at the issue date of the policy, immediately before the premium is paid. [2] (ii) Find the expected value of the random variable you have written down in part (i). 13J [Total 5] Basis: Mortality: PA92C20 Interest 4% paJohn Smith likes driving his car to visit different places. He also has a long drive to work. John spends almost all his spare money driving to one place or another. One of the places he likes to drive to is the local zoo, a five-mile round trip. When he isn't visiting the zoo he tends to go on longer drives to see more distant attractions. When the price of petrol goes up, John Smith is very much worse off. As a result, he goes on fewer trips, particularly longer trips, but also fewer trips to the local zoo. When the local zoo puts up its admission prices from $5 to $6, he goes to the zoo less often, making more trips to more distant attractions instead. The result of higher admission prices at the local zoo is that John consumes more petrol. Comment on John's joint consumption pattern with regard to visits to the zoo and petrol