IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples
X is uniform on (0,10). Given that X exceeds 4, what is the expected value of X?
The conditional expectation is 7. Given X exceeds 4, the distribution is uniform on the interval from 4 to 10, so its mean is the midpoint, 7.
- A7Correct
- B5
- C6
- D3
- 8
Explanation
Conditional on X>4, X is uniform on (4,10), whose mean is (4+10)/2 = 7. The unconditional mean 5 ignores the condition.
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