Question

You are given that claims are reported according to a homogeneous Poisson process. Starting from time...

You are given that claims are reported according to a homogeneous Poisson
process. Starting from time zero, the expected waiting time until the second claim is three
hours. Calculate the standard deviation of the waiting time until the second claim.

Math   Statistics-And-Probability   
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Answer #1

Expected waiting time until the second claim is given here to be 3 hours. Therefore average waiting time for 1 claim is given here as: 3/2 = 1.5 hour.

For the rate of arrival as a poisson distribution, the waiting time distribution would be an exponential distribution with parameter as reciprocal of the mean waiting time. Therefore the distribution of waiting time here is given as:

For exponential distribution the standard deviation is same as mean.

Therefore for 2 claims, the standard deviation would also be 3 hours.

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