IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Stochastic processes
Two independent Poisson processes count health claims (rate 4 per day) and travel claims (rate 1 per day) at an Indian insurer. What is the probability that the first claim arriving is a travel claim, and what is the distribution of the time to the first claim of any type?
The probability is 0.2 and the waiting time is exponential with mean 0.2 days. The merged process has rate 5, travel claims are a fraction 1/5 of events, and the time to the first event is exponential with rate 5.
- A0.2; exponential with mean 0.2 daysCorrect
- B0.2; exponential with mean 1 day
- C0.25; exponential with mean 0.2 days
- D0.8; exponential with mean 0.2 days
- 0.2; exponential with mean 5 days
Explanation
The combined process is Poisson with rate 5. Each event is travel with probability 1/5 = 0.2. The waiting time to the first event is exponential with rate 5, so mean 1/5 = 0.2 days. Option 3 divides 1 by 4 instead of 5.
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