Evie takes the bus to campus. There are two different bus stops near her house, and each is serviced by a different bus route. Busses that arrive at Bus Stop A do so according to a Poisson Process at a rate of 1 buses per hour. Bus Stop B is slightly further from her house, but busses that arrive at Bus Stop B do so according to a Poisson Process at a rate of 5 buses per hour. a) Find the mean and standard deviation of the time (in minutes) that Evic waits for a bus if she decides to go to Bus Stop A. (2 marks) b) Find the mean and standard deviation of the time (in minutes) that Evic waits for a bus if she decides to go to Bus Stop B. (2 marks) c) Calculate the probability that Evic waits between 10 and 20 minutes for a bus to arrive if she decides to go to Bus Stop A. (2 marks) d) If Evic has already been waiting 5 minutes for the bus at Bus Stop B, calculate the probability that she waits no more than 12 minutes total for the bus to arrive. (2 marks) e) Evie decides which bus stop to go to by generating a realization of a continuous Uniform (0,1) with a random number generator. If the value generated is between 0 and 0.5, she goes to Bus Stop A. If the value generated is between 0.5 and 1, she goes to Bus Stop B. What is the probability she waits at a bus stop for at least 10 minutes before a bus arrives