CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
A stock is modeled as a binomial random variable where each day the probability of an up move is 0.6, with independent days. The probability that exactly 2 of 3 days are up moves is closest to:
The probability is about 0.432. It equals 3 combinations times 0.6 squared times 0.4, which is 3 × 0.36 × 0.4. The value 0.648 would be the probability of at least two up days, not exactly two.
- A0.288
- B0.432Correct
- C0.648
Explanation
P(X=2) = C(3,2) × 0.6^2 × 0.4 = 3 × 0.36 × 0.4 = 0.432. The 0.288 option comes from using 0.6×0.4^2×3 (swapping probabilities). The 0.648 figure is P(X≥2) = 0.432 + 0.216.
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