Skip to content

FRM Part I · FRM Exam Part I · Sample Moments

Observations X1, X2, X3 are i.i.d. with mean mu and variance 36. Estimator A is the sample mean (X1+X2+X3)/3. Estimator B is (X1 + 2*X2 + 3*X3)/6. Both are unbiased. What is the variance of B and which estimator is preferred under BLUE?

The weights of B are 1/6, 2/6 and 3/6, so its variance is 36 times 14/36, which is 14. The sample mean has variance 36/3 = 12. Both are unbiased, so the sample mean, with the smaller variance, is preferred.

  1. AVariance of B is 14; B is preferred
  2. BVariance of B is 14; A is preferred
  3. CVariance of B is 42; A is preferredCorrect
  4. DVariance of B is 42; B is preferred

Explanation

Var(B) = 36*(1+4+9)/36 = 14... check: weights are 1/6, 2/6, 3/6, so sum of squared weights = (1+4+9)/36 = 14/36, and Var(B) = 36*14/36 = 14. Var(A) = 36/3 = 12. Hence B's variance is 14, not 42, and A has the lower variance.

Did you get it right without looking?

One question tells you little. A timed set on Sample Moments shows your real accuracy, how long you take and where you lose marks.

Practise Sample MomentsFree diagnostic mock

More Sample Moments questions