IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Stochastic processes
Calls to a Mumbai insurer's helpline form a Poisson process of rate 12 per hour. Given that exactly 3 calls occurred between 10:00 and 10:30, what is the expected number of calls between 10:00 and 10:10?
The expected number is 1. Conditional on three calls in the 30-minute window, each call is uniformly distributed over it, so each lands in the first 10 minutes with probability one third, giving 3 x 1/3 = 1.
- A1Correct
- B2
- C0.5
- D3
- 6
Explanation
Given N=3 in the interval, each call's arrival time is independently uniform on it. Each call falls in the first 10 minutes with probability 1/3. The expected number is 3 x 1/3 = 1. The rate 12 is irrelevant once the count is given.
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