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

Quote:

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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

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

CB