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

A fair six-sided die is rolled once. Let X be the number showing. Under a discrete uniform distribution on {1,2,3,4,5,6}, what is the variance of X?

The variance of a fair die roll is 35/12, or about 2.92, using the discrete uniform formula (n^2 - 1)/12 with n = 6. The figure 3.5 is the mean and 1.71 is the standard deviation, so neither is the variance.

  1. A2.92Correct
  2. B3.50
  3. C2.50
  4. D1.71

Explanation

For a discrete uniform on 1..n, variance = (n^2 - 1)/12 = (36 - 1)/12 = 35/12 = 2.92. The value 3.50 is the mean, not the variance. 1.71 is the standard deviation (sqrt of 2.92). 2.50 would come from wrongly using n(n-1)/12 = 2.5.

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