FRM Part I · FRM Exam Part I · Multivariate Random Variables
Binary variables X and Y are independent. P(X=1)=0.60 and the joint probability P(X=1, Y=1)=0.18. What is the joint probability P(X=0, Y=0)?
The joint probability P(X=0, Y=0) is 0.28. Independence lets the joint equal the product of marginals, so P(Y=1)=0.18/0.60=0.30, P(Y=0)=0.70, and P(X=0)=0.40 gives 0.40 times 0.70, which is 0.28.
- A0.12
- B0.28Correct
- C0.42
- D0.40
Explanation
Independence means P(X=1,Y=1)=P(X=1)P(Y=1), so P(Y=1)=0.18/0.60=0.30 and P(Y=0)=0.70. Then P(X=0,Y=0)=0.40×0.70=0.28. The value 0.12 is P(X=0,Y=1) and 0.42 is P(X=1,Y=0).
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