9. Customers enter a store according to a Poisson process of rate = 6 per hour. Suppose it is known that but a single customer entered during the first hour. What is the conditional probability that this person entered during the first fifteen minutes? 10. Customers arrive at a service facility according to a Poisson process of rate 2=5 per hour. Given that 12 customers arrived during the first two hours of service, what is the conditional probability that 5 customers arrived during the first hour? 11. Shocks occur to a system according to a Poisson process of intensity 2. Each shock causes some damage to the system, and these damages accumulate. Let N(t) be the number of shocks up to time t, and let Y; be the damage caused by the ith shock. Then is X(t)=Y+Y+...+ya the total damage up to time t. Determine the mean and variance of the total damage at time t when the individual shock damages are exponentially distributed with parameter 0.