FRM Part I · FRM Exam Part I · Common Univariate Random Variables
X is continuous uniform on [0, 10]. Given that X is greater than 4, what is the expected value of X?
The conditional expected value is 7.0. Given X exceeds 4, X remains uniform but on the interval from 4 to 10, so its mean is the midpoint, (4+10)/2 = 7. The unconditional mean of 5 ignores the information provided.
- A5.0
- B6.0
- C7.0Correct
- D8.0
Explanation
Conditional on X > 4, X is uniform on [4, 10]. Its mean is (4+10)/2 = 7.0. The unconditional mean of 5.0 ignores the conditioning; 6.0 averages 4 and 8 incorrectly.
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