# Poisson process - emergency call center question

• Oct 5th 2009, 05:19 PM
Flipz4226
Poisson process - emergency call center question
Assume a Poisson process. An emergency call center gets 3 calls per minute average. What is the probability that the second call will come in 30 seconds and before 60 seconds have passed?

This is what I know for sure. Use two poisson variables X and Y and then add them together (maybe using moment generating function?)

X = time it takes for first call to come in
Y = time it takes for second call to come in

I'm not sure how to set up this problem and I guess I should use 3/2 as the poisson parameter? Thanks
• Oct 6th 2009, 04:09 AM
CaptainBlack
Quote:

Originally Posted by Flipz4226
Assume a Poisson process. An emergency call center gets 3 calls per minute average. What is the probability that the second call will come in 30 seconds and before 60 seconds have passed?

This is what I know for sure. Use two poisson variables X and Y and then add them together (maybe using moment generating function?)

X = time it takes for first call to come in
Y = time it takes for second call to come in

I'm not sure how to set up this problem and I guess I should use 3/2 as the poisson parameter? Thanks

In such a process the interval between calls has an exponential distribution with mean time between arrivals of 20 seconds.

CB