IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
A sample of n independent claims is drawn from an Exponential distribution with mean 1000 (rupees). With n = 5, what is the probability that the sample minimum exceeds 400? Give the nearest value.
The minimum exceeds 400 only if all five claims exceed 400. Each has probability e^(-0.4), so the joint probability is e^(-2), approximately 0.1353.
- A0.0183Correct
- B0.1353
- C0.6703
- D0.0067
- 0.4493
Explanation
P(min > 400) = [P(X > 400)]^5 = (e^{-0.4})^5 = e^{-2} = 0.1353. The question asks about 5 claims: e^{-0.4*5} = e^{-2} = 0.1353, so the key must be 0.1353.
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