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Answer: Mean = 0.85, standard deviation = 0.84
## Explanation This is a binomial distribution problem where: - Number of trials (n) = 5 bonds - Probability of success (default) p = 0.17 - Probability of failure (no default) q = 1 - p = 0.83 **Mean (μ) calculation:** μ = n × p = 5 × 0.17 = 0.85 **Standard deviation (σ) calculation:** σ = √(n × p × q) = √(5 × 0.17 × 0.83) = √(0.7055) ≈ 0.84 Therefore, the correct answer is: - Mean = 0.85 - Standard deviation = 0.84 This corresponds to option B.
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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