FRM Part I · FRM Exam Part I · Multivariate Random Variables
The joint probability mass function of discrete variables X (values 0, 1) and Y (values 1, 2) is: P(X=0,Y=1)=0.10, P(X=0,Y=2)=0.30, P(X=1,Y=1)=0.25, P(X=1,Y=2)=0.35. What is the marginal probability that Y = 2?
The marginal probability that Y equals 2 is 0.65. It is found by summing the joint probabilities across all values of X: 0.30 for X=0 and 0.35 for X=1. Using only one cell gives a joint, not a marginal, probability.
- A0.30
- B0.35
- C0.65Correct
- D0.35 divided by 0.60
Explanation
The marginal probability of Y=2 sums the joint probabilities over all X values: 0.30 + 0.35 = 0.65. The option 0.35 uses only X=1, ignoring the X=0 cell. The last option is a conditional probability P(X=1|Y=2) type calculation and uses the wrong denominator.
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