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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, which follows a discrete uniform distribution on {1, 2, 3, 4, 5, 6}. What is the variance of X?

The variance is 2.92. For a discrete uniform variable on 1 to n, variance equals (n squared minus 1) divided by 12, so (36 - 1)/12 = 35/12 = 2.92. The figure 3.50 is the mean and 1.71 is the standard deviation.

  1. A2.92Correct
  2. B3.50
  3. C2.67
  4. D1.71

Explanation

For a discrete uniform on integers 1 to n, variance = (n^2 - 1)/12 = (36 - 1)/12 = 35/12 = 2.92. The value 3.50 is the mean, not the variance. The value 1.71 is the standard deviation (sqrt of 2.92).

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