FRM Part I · FRM Exam Part I · Multivariate Random Variables
The joint probability mass function of X and Y is: P(X=0,Y=0)=0.20, P(X=0,Y=1)=0.30, P(X=1,Y=0)=0.10, P(X=1,Y=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, so dividing 0.40 by 0.50 gives 0.80.
- A0.40
- B0.50
- C0.80Correct
- D0.57
Explanation
P(X=1)=0.10+0.40=0.50. P(Y=1|X=1)=0.40/0.50=0.80. The value 0.40 is the joint probability, not conditioned on X=1. The value 0.57 is P(X=1|Y=1)=0.40/0.70.
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