FRM Part I · FRM Exam Part I · Multivariate Random Variables
X takes values 1 or 2 and Y takes values 10 or 20 with joint probabilities: P(1,10)=0.30, P(1,20)=0.20, P(2,10)=0.10, P(2,20)=0.40. What is E[Y | X = 1]?
E[Y | X=1] equals 14. Given X=1, the conditional probabilities of Y=10 and Y=20 are 0.6 and 0.4 after dividing the joint probabilities by P(X=1)=0.5, so the conditional mean is 10(0.6)+20(0.4)=14.
- A7
- B14Correct
- C16
- D18
Explanation
P(X=1)=0.30+0.20=0.50. The conditional probabilities are 0.6 for Y=10 and 0.4 for Y=20, so E[Y|X=1] = 6 + 8 = 14. The value 16 is the unconditional E[Y] and 7 forgets to divide by P(X=1).
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