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罗小胖 · 2023年10月05日

为什么,没懂

NO.PZ2022062760000012

问题如下:

An analyst is examining a portfolio that consists of 1,000 subprime mortgages and 600 prime mortgages. Of the subprime mortgages, 200 are late on their payments. Of the prime mortgages, 48 are late on their payments. If the analyst randomly selects a mortgage from the portfolio and it is currently late on its payments, what is the probability that it is a subprime mortgage?

选项:

A.

60%

B.

67%

C.

75%

D.

81%

解释:

中文解析:

首先计算任何一个mortgage late的概率

P(Mortgage is late) = (200+48)/(1000+600) = 15.5%

利用贝叶斯公式:

P(Subprime mortgage | Mortgage is late) = P(Subprime mortgage and late)/P(Mortgage is late).

已知:

P(Subprime mortgage and late) = 200/1600 = 12.5%;

得:

P(Subprime mortgage | Mortgage is late) = 12.5% / 15.5% = 0.81 = 81%

In order to solve this conditional probability question, first calculate the probability that any one mortgage in the portfolio is late.

This is: P(Mortgage is late) = (200+48)/(1000+600) = 15.5%.

Next, use the conditional probability relationship as follows:

P(Subprime mortgage | Mortgage is late) = P(Subprime mortgage and late)/P(Mortgage is late).

Since P(Subprime mortgage and late) = 200/1600 = 12.5%;

P(Subprime mortgage | Mortgage is late) = 12.5% / 15.5% = 0.81 = 81%.

Hence the probability that a random late mortgage selected from this portfolio turns out to be subprime is 81%.

这道题能用画图,两步骤的方式来做么

1 个答案
已采纳答案

李坏_品职助教 · 2023年10月05日

嗨,努力学习的PZer你好:


根据贝叶斯公式:

这道题就是让我们去求在已知“ late on its payments”的情况下,该样本属于subprime mortgage的概率是多少?


设:“late on payments”就是事件B,“属于subprime mortgage”是事件A。题目让求的就是P(A|B)


P(A|B) = P(AB) / P(B),这里P(AB)就是某个贷款既属于A又属于B的概率,只有200个样本是既属于A有属于B。P(AB)=200/1600=12.5%,

而P(B)是B发生的概率,也就是某个贷款late on payments的概率,一共是248个late的,所以P(B)=248/1600=15.5%,

所以P(A|B) = P(AB)/(PB) = 12.5%/15.5% = 81%.


建议同学去听一下quant部分Bayes’ Formula 的两个example

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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