Verified solution · Exam P
This Exam P sample reference tests Joint Probability Functions. This is the correlation of two binary variables from a four-cell joint distribution. Their covariance is 1/16 and the product of their standard deviations is √(15)/16, so the correlation is 1/√(15)=0.2582 and choice C.
Independent solution
Setup
For binary variables, each first moment is its probability of taking value one, while XY equals one only in the joint one-one cell.
Model
Use Bernoulli variances for the marginals and center the product moment for covariance.
Compute
Normalize the covariance by the two marginal standard deviations.
Answer
The correlation rounds to 0.26.
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Original practice · fully worked
Let A indicate that a technician has advanced certification and let B indicate that the technician completes a repair within the target time. In a workforce, P(A=1)=0.40, P(B=1 given A=1)=0.70, and P(B=1 given A=0)=0.20. Calculate the correlation coefficient of A and B.
The conditional rates give P(B=1)=0.40 and P(A=1,B=1)=0.28. Thus the covariance is 0.12, both marginal variances are 0.24, and the correlation is 0.12/0.24=0.5000, so choice D.
Setup
Convert the conditional completion rates into a joint success probability and the marginal probability for B.
Model
Because A and B are indicators, their expectations equal their success probabilities.
Compute
Center the product moment, then divide by the marginal standard deviations.
Answer
The indicator correlation is 0.5000.
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Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
