Poisson 1

Poisson 1 - 1 Trains arrive at a train station at a rate of...

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1. Trains arrive at a train station at a rate of 1 every 30 minutes. a. Calculate the probability that at least two trains arrive in the first hour, but no more than three trains arrive in the first two hours. b. Calculate the probability that at least two trains arrive in the first hour, and at least 3 trains arrive in the first two hours. 2. There are two types of trains that arrive at a train station. Express trains arrive at a rate of 1 per hour while local trains arrive at a rate of 3 per hour. Calculate the probability that at least four trains arrive at the station in the next hour with no more than two of the trains being express trains. 3. There are two types of trains that arrive at a train station. Express trains arrive at a rate of 1 per hour while local trains arrive at a rate of 3 per hour. Given that exactly three trains arrive at the station in the next hour, calculate the probability that at least two of the trains are express trains.

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