IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
A population of 5 policies has claim amounts (in Rs thousand) 2, 4, 6, 8 and 10. A simple random sample of size 2 is drawn without replacement, with all pairs equally likely. Which of the following is the variance of the sample mean?
The variance of the sample mean is 3.0. The population variance with divisor N is 8, and sampling without replacement gives (8/2) multiplied by the finite population correction (5-2)/(5-1) = 0.75, which equals 3. Ignoring the correction gives 4.
- A1.0
- B2.0
- C3.0Correct
- D4.0
- 5.0
Explanation
Population mean is 6 and the population variance (divisor N) is (16+4+0+4+16)/5 = 8. Without replacement, Var = (sigma^2/n)(N-n)/(N-1) = (8/2)(3/4) = 3. The value 4 ignores the finite population correction.
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