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.
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?