CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
A binomial random variable has n = 20 trials and probability of success p = 0.25. The expected value and variance of the number of successes are most likely:
The expected value is 5 and the variance is 3.75. The mean is n times p, which is 20 × 0.25, and the variance is n times p times (1−p), which is 20 × 0.25 × 0.75.
- AExpected value 5; variance 3.75Correct
- BExpected value 5; variance 5.00
- CExpected value 15; variance 3.75
Explanation
Mean = np = 20 × 0.25 = 5. Variance = np(1−p) = 20 × 0.25 × 0.75 = 3.75. Variance of 5 ignores the (1−p) factor; mean 15 uses 1−p instead of p.
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