FRM Part I · FRM Exam Part I · Random Variables
A discrete random variable X takes the value 1 with probability 0.5, the value 2 with probability 0.3 and the value 5 with probability 0.2. What is the variance of X?
The variance is 2.29. The mean is 2.1 and the second raw moment is 6.7, so variance equals 6.7 minus 2.1 squared, or 6.7 minus 4.41. Reporting 6.7 would ignore the subtraction of the squared mean.
- A2.29Correct
- B6.70
- C2.10
- D1.51
Explanation
E[X] = 0.5(1) + 0.3(2) + 0.2(5) = 2.1. E[X^2] = 0.5(1) + 0.3(4) + 0.2(25) = 6.7. Variance = 6.7 - 2.1^2 = 6.7 - 4.41 = 2.29. The value 6.70 is the second raw moment, which is wrong because the squared mean was not subtracted.
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