Question 3 (40%) Consider a hypothetical Green Line D train schedule at reservoir that (during normal hours) on average for both directions a D train will pass the station every 10 minutes. Assume that such schedule satisfies the assumptions for exponential distribution.1 1 Also, assume that passengers who go aboard or get off the D train take no time.i. What is the probability that someone who arrives at the station during normal hours and waits for less than =1 minutes to go aboard an inbound D train? ii. What is the probability that someone who arrives at the station during normal hours and waits for more than 15 minutes to go aboard an outbound D train? iii. Assume that the inbound and outbound D trains operate independently. What is the probability that during normal hours no D train passes the station for more than 1U minutes? iv. Assume now that the D train has a xed schedule and [although uhliloely} never delays or departs early. For every 11] minutes there will he an inbound D train passing the station.r and for every l minutes there will also he an outbound D train passing the station. A hypothetical man arrives at the station everyday at a random time point during the normal hours and will either go to see his girlfriend who lives at Copley or his mother who lives at Newton Center. The man always takes the rst coming D train. It turns out that 39% of the time the man goes to his girlfriend. Explain why it is the ease