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

A random variable X is continuously uniformly distributed on the interval [20, 60]. What are its mean and variance?

The mean is 40 and the variance is 133.33. For a continuous uniform variable on [a, b], the mean is (a+b)/2 and the variance is (b-a)^2/12, giving 40 and 1600/12 respectively.

  1. AMean 40, variance 133.33Correct
  2. BMean 40, variance 100.00
  3. CMean 40, variance 1,600
  4. DMean 30, variance 133.33

Explanation

Mean = (20+60)/2 = 40. Variance = (b-a)^2/12 = 40^2/12 = 1600/12 = 133.33. Using 100 would result from dividing by 16 rather than 12, and 1,600 omits the division entirely.

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