FRM Part I · FRM Exam Part I · Common Univariate Random Variables
A random variable X is continuous uniformly distributed on the interval [20, 60]. What is the variance of X?
The variance of a continuous uniform variable on [20, 60] is (60-20)^2/12 = 1,600/12, which equals 133.33. The formula divides the squared interval width by 12, so the other values result from using the wrong divisor or forgetting it.
- A100.00
- B133.33Correct
- C160.00
- D1,600.00
Explanation
Variance of a uniform variable is (b-a)^2/12 = (40)^2/12 = 1,600/12 = 133.33. Option 1,600 omits the division by 12; 160 wrongly divides by 10; 100 uses a different wrong divisor (16).
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