FRM Part I · FRM Exam Part I · Random Variables
A random variable X has E[X] = 3 and Var(X) = 4. What is E[X^2]?
E[X^2] equals the variance plus the squared mean: 4 + 3^2 = 13. Subtracting the squared mean would give a wrong figure, since variance is E[X^2] minus the square of E[X].
- A7
- B13Correct
- C16
- D10
Explanation
Var(X) = E[X^2] - (E[X])^2, so E[X^2] = 4 + 9 = 13. Option 7 subtracts instead of adding, and 10 uses 4+6, a wrong step.
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