Financial Risk Manager Part 1

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Explanation:

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.

Explanation:

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.

Comments (1)

Yash ParwaniMar 17, 2026 6:22 AM

The option is wrong. The correct options should be B as it is asked for standard deviation

LeetQuiz .Mar 19, 2026 4:52 PM

Hi Yash, Thanks for your pointing out. I've correct answer to be option B. Your feedback help us keep improving the quality of question. Appreciated !

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?

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Last updated: March 19, 2026 at 16:53

Mean = 0.15, standard deviation = 0.71

19.4%

Mean = 0.85, standard deviation = 0.84

38.7%

Mean = 0.85, standard deviation = 0.71

35.5%

Mean = 0.15, standard deviation = 0.84

6.5%

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Comments (1)

Yash ParwaniMar 17, 2026 6:22 AM

The option is wrong. The correct options should be B as it is asked for standard deviation

LeetQuiz .Mar 19, 2026 4:52 PM

Hi Yash, Thanks for your pointing out. I've correct answer to be option B. Your feedback help us keep improving the quality of question. Appreciated !