IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Stochastic processes
Claims arrive at an Indian motor insurer as a Poisson process with rate 6 per hour. What is the probability that no claim arrives in a 20-minute interval?
The probability is e^-2, about 0.135. Over 20 minutes, one third of an hour, the Poisson mean is 6 x 1/3 = 2 claims, and the chance of zero claims is e raised to minus that mean.
- Ae^-2 ≈ 0.135Correct
- Be^-6 ≈ 0.0025
- Ce^-20 ≈ 0
- D1 - e^-2 ≈ 0.865
- 2e^-2 ≈ 0.271
Explanation
20 minutes is 1/3 hour, so the expected number of claims is 6 x 1/3 = 2. P(N=0) = e^-2 ≈ 0.135. Option 1 uses the full hourly rate, and option 3 is the probability of at least one claim.
Did you get it right without looking?
One question tells you little. A timed set on Stochastic processes shows your real accuracy, how long you take and where you lose marks.
More Stochastic processes questions
- A Markov jump process models a policyholder in states H (healthy), S (sick) and D (dead). Transition rates per year are: H to S 0.10, H to D…
- A simple random walk starts at 0. At each step it moves up 1 with probability 0.6 and down 1 with probability 0.4, independently. What is th…
- A Markov jump process has states 1 (healthy), 2 (sick) and 3 (dead, absorbing). Constant rates: σ12 = 0.2, σ13 = 0.05, σ21 = 0.4, σ23 = 0.1 …
- Which statement about a finite, irreducible, aperiodic Markov chain is correct?
- A process is observed at all real times t ≥ 0, and at each time it takes one of the values in the finite set {Healthy, Sick, Dead}. How is t…
- Claims follow a Poisson process with rate 3 per month. Each claim is independently a large claim with probability 0.2. Let X be the number o…