Answer-first summary for fast verification
Answer: Mean = 0.85, standard deviation = 0.84
For a binomial distribution: - Mean (μ) = n * p = 5 * 0.17 = 0.85 - Variance = n * p * (1-p) = 5 * 0.17 * 0.83 = 0.7055 - Standard deviation (σ) = √0.7055 ≈ 0.84 Wait, let me recalculate: - Mean = 5 * 0.17 = 0.85 - Variance = 5 * 0.17 * 0.83 = 0.7055 - Standard deviation = √0.7055 ≈ 0.84 Actually, looking at the options, option B has mean = 0.85 and standard deviation = 0.84, which matches my calculation. But let me check option C: mean = 0.85, standard deviation = 0.71. √0.7055 ≈ 0.84, not 0.71. Therefore, the correct answer should be **B** with mean = 0.85 and standard deviation = 0.84.
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Q-27. A portfolio manager holds five bonds in a portfolio and each bond has a 1-year default probability of 17%. The event of default for each of the bonds is independent. What is the mean and standard deviation of the number of bonds defaulting over the next year?
A
Mean = 0.15, standard deviation = 0.71
B
Mean = 0.85, standard deviation = 0.84
C
Mean = 0.85, standard deviation = 0.71
D
Mean = 0.15, standard deviation = 0.84
