IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Loss distributions, with and without risk sharing
Claim amounts on a motor portfolio follow an exponential distribution with mean Rs 20,000. What is the probability that a claim exceeds Rs 50,000?
The probability is e^(-2.5). With mean 20,000 the exponential survival function is exp(-x/20,000), and at x = 50,000 the exponent is -2.5. The other options invert the ratio or give the complementary probability of a claim below 50,000.
- Ae^(-0.4)
- Be^(-1.0)
- Ce^(-2.5)Correct
- D1 - e^(-2.5)
- e^(-2.5) / 2
Explanation
The exponential rate is 1/20,000, so P(X > 50,000) = exp(-50,000/20,000) = e^(-2.5). Option e^(-0.4) wrongly uses 20,000/50,000. Option 1 - e^(-2.5) is the probability of being below 50,000, not above it.
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