Thread: Probability 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.

Originally Posted by ulysses123

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.

The number that arrive in a two day period has a Poission distribution with rate 6 per period.

So now your question is what is the probability of 4 or fewer trains arrive in a two day period.

CB

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?

Originally Posted by ulysses123

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?

That will be because you have to compute:

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

doing the way you suggest.

CB