Problem 2 A. Eli enters the subway station at 9a.m. on Monday. The waiting time for the train is a random variable that follows an exponential distribution. If there is an equipment breakdown, the average waiting time is 40 minutes. If lines are functioning properly, the average waiting time is 10 minutes. During weekday commute times, the chance of subway malfunctions is 7%. He waited 25 minutes until the train showed up. What is the probability there was an equipment issue? B. He also enters the subway at 11a.m. on Saturday. There is a 40% chance of subway malfunctions over the weekends. He again waited 25 minutes until the train showed up. What is the probability now that there was an equiment issue? Exponential distribution This is a continuous distribution which is used to model event waiting or interarrival times. It has one parameter , which is the average waiting time. Some useful facts: - Probability density is Pr[X = t] = %exp(%) and cumulative density is Pr[X g t] = 1 exp(%) - Expectation is EL\" 2 and variance is Var[X] = z