IAI Actuarial Core Principles · Actuarial Statistics · Expectations and conditional expectations
X and Y are random variables with E[Y | X] = 3X + 2. Given E[X] = 4, what is E[Y]?
E[Y] equals 14. Using the law of total expectation, E[Y] = E[3X + 2] = 3 times E[X] plus 2, which is 3 times 4 plus 2 = 14. The constant term must be included, so 12 is wrong.
- A12
- B14Correct
- C16
- D18
- 10
Explanation
By the tower property E[Y] = E[E[Y|X]] = 3E[X] + 2 = 3(4) + 2 = 14. Option 12 omits the constant 2. Option 16 wrongly adds 2 twice or uses a wrong multiplier.
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