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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

Two independent normal samples of equal-risk portfolios give sample variances of 0.0036 (n = 11) and 0.0016 (n = 9). The analyst forms F = larger variance / smaller variance to test equal variances. Which statement is correct?

F equals 2.25 with 10 numerator and 8 denominator degrees of freedom. The ratio of 0.0036 to 0.0016 is 2.25, and each degree of freedom is the sample size minus one, matched to the sample whose variance is in that position.

  1. AF = 2.25 with 8 numerator and 10 denominator degrees of freedom
  2. BF = 0.44 with 10 and 8 degrees of freedom
  3. CF = 2.25 with 10 numerator and 8 denominator degrees of freedomCorrect
  4. DF = 1.50 with 10 and 8 degrees of freedom

Explanation

F = 0.0036/0.0016 = 2.25. The numerator sample is the larger variance with n = 11, so df = 10; the denominator has n = 9, so df = 8. Swapping df mismatches the samples; 1.50 is the ratio of standard deviations.

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