I am facing the following problem:
In an insurance company, one models claim occurrences of a given insurance portfolio by a Poisson process with intensity parameter \lambda$=52 (time is supposed to be measured in years).
1) What is the average time interval between two claim occurrences?
I guess I have to take the expected value of the exponential distribution with parameter 1/52.
2) Assuming that no claim occurred during the first 5 weeks, what is the expected number of claims occurring in the next 47 weeks of the year? What becomes this expected number if one supposes that we observed 5 claims during the first 5 weeks?
How to solve this one? I don't know how to put it in equations :s
1) Yep.
2) Memoryless property implies these are the same. The number of events in a window of length $t$ is Poisson($\lambda t$) distributed.