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IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions

A random sample of size 10 is drawn from a normal population with mean 50 and variance 16. Let S^2 be the sample variance (divisor n-1). What is the variance of S^2?

Var(S^2) equals 2 sigma^4 divided by (n-1), which is 2 x 256 / 9, about 56.89.

  1. A3.56
  2. B6.40
  3. C28.44Correct
  4. D32.00
  5. 256.00

Explanation

(n-1)S^2/sigma^2 follows chi-square with 9 degrees of freedom, variance 18. So Var(S^2) = (sigma^2/9)^2 x 18 = 2 sigma^4/9 = 2 x 256/9 = 56.89? Check: Var(S^2)=2 sigma^4/(n-1)=2x256/9=56.89. Correct computation: sigma^2=16, sigma^4=256, 512/9=56.89, which is not listed, so see directAnswer.

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