A train bridge is constructed across a wide river. Trains arrive according to a poisson process of rate lambda=3 per day.

Find the probability that it takes more than 2 days for the 5th train to arrive at the bridge.

Printable View

- March 14th 2011, 10:17 PMulysses123Probability question
A train bridge is constructed across a wide river. Trains arrive according to a poisson process of rate lambda=3 per day.

Find the probability that it takes more than 2 days for the 5th train to arrive at the bridge. - March 15th 2011, 12:14 AMCaptainBlack
- March 15th 2011, 12:35 AMulysses123
in our book we have that the time of the kth arrival is a gamma distribution. I did it by evaluating the gamma distribution P(T(5)>2)=

1-P(T(5)<=2)=1-(P(T5=0)+P(T5=1)+P(T5=2)

this however gives me a difference answer to what i get doing it the way you sugested as a poison process with rate 6.

can anyone else check if the two mwthods give the same answer? - March 15th 2011, 05:21 AMCaptainBlack