IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
Independent samples of sizes 6 and 11 come from normal populations with equal variances. If S1^2 and S2^2 are the sample variances, S1^2/S2^2 follows an F distribution with which degrees of freedom, and what is the mean of that F?
The ratio is F with (5,10) degrees of freedom, and its mean is 10/(10-2) = 10/8 = 1.25.
- A(6,11) and mean 11/9
- B(5,10) and mean 10/8Correct
- C(5,10) and mean 5/10
- D(6,11) and mean 6/11
- (5,10) and mean 10/9
Explanation
Degrees of freedom are n-1: 5 for the numerator and 10 for the denominator. The mean of F(a,b) is b/(b-2) = 10/8 = 1.25.
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