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Poisson 2

# Poisson 2 - 1 Trains arrive at a station at a rate of 6 per...

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1. Trains arrive at a station at a rate of 6 per hour. a. Calculate the expected time until the arrival of the first train. b. Calculate the variance around the wait time for the first train. c. Calculate the expected time of arrival of the 10 th train. d. Calculate the variance of the expected arrival time for the 10 th train. e. If you ride the train to work every working day for a year, using the normal approximation, calculate maximum amount of time that you could spend waiting during the year with a 95% confidence level. There are 200 working days in a year. 2. There are two types of trains that arrive at a train station. Express trains arrive at a rate of 6 per hour while local trains arrive at a rate of 12 per hour. An express takes 15 minutes to get to downtown Chicago while it takes a local train takes 25 minutes. a. You are waiting in the train station for a train. If you take the first train that arrives, what is your expected time until arrival (including the wait time).

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