1)The number of DC Metro trains arriving per hour during rush hour at a particular station is distributed Poisson, with a mean of 6 trains.

i.What is the probability that exactly 8 trains will arrive in an hour during rush hour on a random Tuesday?

ii.You are standing at the station during rush hour and hoping that your train will arrive in the next 15 minutes. Since trains arrive in both directions, you hope that two trains will arrive so at least one is going your way. What is the probability that at least two trains will arrive in the next 15 minutes?

iii.What is the average time between train arrivals, in minutes?

ix. What is the probability that the next train will arrive sometime within the next 10 minutes?