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。。 · 2025年07月09日

这道题应该用那个分布计算

NO.PZ2023091601000034

问题如下:

Anoperational risk manager uses the Poisson distribution to estimate thefrequency of losses in excess of USD 2 million during the next year. It isobserved that the frequency of losses greater than USD 2 million is three peryear on average over the last 10 years. Assuming that this observation isindicative of future occurrences and that the probability of one eventoccurring is independent of all other events, what is the probability of fivelosses in excess of USD 2 million occurring during the next two years?

选项:

A.

10.08%

B.

14.04%

C.

14.62%

D.

16.06%

用指数分布好像也不行,泊松分布无从下手

1 个答案

李坏_品职助教 · 2025年07月09日

嗨,从没放弃的小努力你好:


题目开头说了,An operational risk manager uses the Poisson distribution to estimate the frequency of losses ,这里告诉你要用泊松分布(Poisson distribution)。


平均来看,每年损失大于2million的数量是3个。 单位时间是1年,在单位时间内发生损失的数量为3,意味着λ = 3.

最后问你,在接下来2年内,损失大于2million的数量为5个的概率是多少?


泊松分布的概率为:

其中,k 是事件发生次数(本题中 k=5),

λ 是单位时间内(1年内)的平均发生率(本题中 λ=3次)

t 是时间跨度(本题中 t=2年),


最后求解:

最后得出是16.06%,正确答案是D。


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