FRM Part I · FRM Exam Part I · Common Univariate Random Variables
A risk manager models the number of defaults among 10 independent loans, each with a default probability of 0.10. What are the mean and variance of the number of defaults?
The mean is 1.0 and the variance is 0.9. For a binomial variable the mean is np, which is 10 times 0.10, and the variance is np(1-p), which is 10 times 0.10 times 0.90. Variance equals mean only for a Poisson variable.
- AMean 1.0, variance 0.9Correct
- BMean 1.0, variance 1.0
- CMean 0.9, variance 1.0
- DMean 10.0, variance 0.9
Explanation
For a binomial, mean = np = 10 x 0.10 = 1.0 and variance = np(1-p) = 10 x 0.10 x 0.90 = 0.9. Setting variance equal to the mean (1.0) is the Poisson property, which does not hold for a binomial.
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