FRM Part I · FRM Exam Part I · Multivariate Random Variables
A multinomial experiment has three outcomes with probabilities 0.5, 0.3 and 0.2. In 10 independent trials, what is the probability of observing exactly 5, 3 and 2 occurrences respectively?
The probability is about 0.0850. The multinomial coefficient is 10!/(5!3!2!) = 2520, and the probability of each specific sequence is 0.5^5 × 0.3^3 × 0.2^2 = 0.00003375, giving 2520 × 0.00003375 ≈ 0.0851.
- A0.0850
- B0.0567Correct
- C0.1000
- D0.1062
Explanation
Coefficient = 10!/(5!3!2!) = 2520. Probability = 2520 × 0.5^5 × 0.3^3 × 0.2^2 = 2520 × 0.03125 × 0.027 × 0.04 = 2520 × 0.000033750 = 0.08505. So the exact value is 0.0851, which is not offered as such; recheck: 0.03125×0.027=0.00084375; ×0.04=0.00003375; ×2520=0.08505. The nearest listed option is A (0.0850).
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