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

An analyst compares the variance of returns of two independent normal portfolios. Portfolio A has sample variance 0.0090 from 16 observations; Portfolio B has sample variance 0.0036 from 21 observations. The F-statistic is formed with the larger sample variance in the numerator. What is the statistic and its degrees of freedom (numerator, denominator)?

F equals 2.50 with 15 and 20 degrees of freedom. The ratio of the larger variance 0.0090 to the smaller 0.0036 is 2.5, and the degrees of freedom are n-1 for each sample, 15 for the numerator portfolio A and 20 for the denominator portfolio B.

  1. AF = 2.50 with (15, 20) degrees of freedomCorrect
  2. BF = 2.50 with (20, 15) degrees of freedom
  3. CF = 0.40 with (15, 20) degrees of freedom
  4. DF = 1.58 with (15, 20) degrees of freedom

Explanation

F = 0.0090/0.0036 = 2.50, with numerator df = 16-1 = 15 and denominator df = 21-1 = 20. Swapping the degrees of freedom (20, 15) mismatches them to the variances. The 1.58 option is the ratio of standard deviations, which is √2.5.

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