FRM Part I · FRM Exam Part I · Common Univariate Random Variables
A loan has a 4% probability of defaulting over one year. Define a Bernoulli random variable X equal to 1 if the loan defaults and 0 otherwise. What is the standard deviation of X?
The standard deviation is 0.1960. A Bernoulli variable has variance p(1-p) = 0.04 x 0.96 = 0.0384, and its square root is about 0.196. The figure 0.0384 is the variance, not the standard deviation.
- A0.0384
- B0.1960Correct
- C0.0400
- D0.0016
Explanation
Variance = p(1-p) = 0.04 x 0.96 = 0.0384. Standard deviation = sqrt(0.0384) = 0.1960. The value 0.0384 is the variance, 0.04 is the mean, and 0.0016 is p squared.
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