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FRM Part I · FRM Exam Part I · Multivariate Random Variables

The joint probability mass function of discrete random variables X (values 0, 1) and Y (values 0, 1, 2) is: P(0,0)=0.10, P(0,1)=0.20, P(0,2)=0.10, P(1,0)=0.15, P(1,1)=0.25, P(1,2)=0.20. What is the marginal probability P(Y = 1)?

The marginal probability that Y equals 1 is 0.45. A marginal probability is found by summing the joint probabilities across every value of the other variable, so 0.20 (X=0) plus 0.25 (X=1) gives 0.45.

  1. A0.25
  2. B0.45Correct
  3. C0.55
  4. D0.20

Explanation

The marginal probability sums the joint probabilities over all values of X: P(Y=1) = P(0,1) + P(1,1) = 0.20 + 0.25 = 0.45. Choosing 0.25 uses only the X=1 cell, and 0.55 is the complement, P(Y≠1).

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