Solve the following questions clearly explaining your answers.

John, aged exactly 35, buys a term assurance policy that pays a benefit of $100,000 at the end of the year of his death if he dies before age 65. What is the expected accumulated value of the benefits at time 10? Basis: AM92 Ultimate, 6% pa interestOn a particular run of a process which bottles a drink, it is thought that the cleansing process of the bottles has partially failed. The bottles have been boxed into crates, each containing six bottles. It is thought that each bottle, independently of all others, has the same chance of containing impurities. A survey has been conducted, and each bottle in a random sample of 200 crates has been tested for impurities. The table below gives the numbers of crates in the sample which had the respective number of bottles which contained impurities. Number of impure bottles: 0 2 3 5 Number of crates: 38 70 58 25 6 N Test the goodness of fit of a binomial distribution to these observations.1. Consider the following constrained two-period optimization problem: max u(C1, (2) = - exp(-701) - Bexp(-702) (1) subject to: al R (2) where y > 0 is the coefficient of absolute risk aversion (CARA), Be (0, 1) is the discount factor, (c1, c2) is the optimal bundle of consumption in periods 1 and 2, / is the given total income during the two periods, R is the gross interest rate. (a) Set up the Lagrangian function for the above optimization problem, and derive the first order conditions