a) A machine is insured against failure. The lifetime of the machine is normally distributed with mean = T years and s.d.= 2 years. An insurance company pays a: dollars if the machine fails the rst or the second year. It pays c/Z dollars if the machine fails in the third or fourth year. After the fourth year, the insurance company pays out nothing. How do you choose a so that the expected value of the payment per insurance is $50? [You can leave your answer as a function of the standard normal CDF} b] The random variable X and Y have a joint density function. The random variable Y takes positive values with mean 1 and variance =2. The conditional distribution of X given Y=y is Unifome distributed (1-y. 1+y} for any y. What is E00 and VariX]