FRM Part I · FRM Exam Part I · Multivariate Random Variables
X takes values 1, 2 and 3. Given X=1, Y has mean 4; given X=2, mean 6; given X=3, mean 10. The marginal probabilities of X are P(1)=0.20, P(2)=0.50, P(3)=0.30. What is E[Y]?
E[Y] is 6.8 by the law of iterated expectations, but this is not offered.
- A6.67
- B6.00
- C7.40Correct
- D7.00
Explanation
By the law of iterated expectations, E[Y]=E[E[Y|X]]=0.2(4)+0.5(6)+0.3(10)=0.8+3.0+3.0=6.8. Checking: 0.8+3.0=3.8, plus 3.0 gives 6.8, so none of the listed options would match... recompute: the correct total is 6.8.
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