IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to extreme value theory
Losses are independent and uniformly distributed on (0, 1) (in Rs crore). For a block of n = 5 losses, what is the expected value of the block maximum?
The expected maximum of n independent uniform(0,1) losses is n/(n+1). With five losses this is 5/6, about 0.8333 crore. It follows from integrating x times the density 5x^4 over zero to one.
- A0.5000
- B0.7500
- C0.8333Correct
- D0.9000
- 0.6667
Explanation
The maximum has distribution function x^5 on (0,1), so its density is 5x^4. The mean is the integral of 5x^5 from 0 to 1, which is 5/6 = 0.8333. Option 0.5 would be the mean of a single loss.
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