FRM Part I · FRM Exam Part I · Multivariate Random Variables
The joint probability distribution of X (0 or 1) and Y (0 or 1) is: P(0,0)=0.30, P(0,1)=0.20, P(1,0)=0.10, P(1,1)=0.40. What is P(Y=1 | X=1)?
The conditional probability is 0.80. The marginal probability that X equals 1 is 0.50, and the joint probability of X=1 and Y=1 is 0.40. Dividing the joint by the marginal gives 0.40/0.50 = 0.80.
- A0.40
- B0.50
- C0.80Correct
- D0.67
Explanation
P(X=1)=0.10+0.40=0.50. P(Y=1|X=1)=P(1,1)/P(X=1)=0.40/0.50=0.80. The value 0.40 is the joint probability, which fails to divide by the marginal. The value 0.67 is P(X=1|Y=1)=0.40/0.60, which conditions on the wrong variable.
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