FRM Part I · FRM Exam Part I · Multivariate Random Variables
The joint probability distribution of two discrete random variables X and Y is: P(X=0,Y=0)=0.20, P(X=0,Y=1)=0.20, P(X=1,Y=0)=0.10, P(X=1,Y=1)=0.50. What is the conditional probability P(Y=1 | X=1)?
The conditional probability is 0.833. The marginal probability that X equals 1 is 0.60, and the joint probability of X=1 and Y=1 is 0.50, so dividing 0.50 by 0.60 gives 0.833. Using 0.50 alone ignores conditioning on X.
- A0.50
- B0.60
- C0.714
- D0.833Correct
Explanation
P(X=1)=0.10+0.50=0.60. P(Y=1|X=1)=0.50/0.60=0.833. The value 0.50 is the unconditional joint probability, not divided by P(X=1). The value 0.714 is P(X=1|Y=1)=0.50/0.70, which reverses the conditioning.
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