IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
A sample of n = 3 is taken from an Exponential distribution with mean 10 (rate 0.1). What is the expected value of the sample minimum?
The expected minimum is 3.33. The minimum of three independent exponentials with rate 0.1 is exponential with rate 0.3, so its mean is 1/0.3, which is about 3.33.
- A10
- B5
- C3.33Correct
- D1.11
- 30
Explanation
The minimum of n independent Exponential(λ) variables is Exponential(nλ). Here the rate is 3 × 0.1 = 0.3, so the mean is 1/0.3 = 3.33. Using 10/2 = 5 would be a miscount of n.
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