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摇一摇 · 2023年08月07日

这句话不太理解，希望老师解释下

  1. CFA I
  2. Quantitative

NO.PZ2021062201000006

问题如下：

In a typical year, 5% of all CEOs are fired for "performance" reasons. Assume that CEO performance is judged according to stock performance and that 50% of stocks have above-average returns or "good" performance. Empirically, 30% of all CEOs who were fired had "good" performance.

Using Bayes' formula, what is the probability that a CEO will be fired given "good" performance? (Hint, let P(A) be the probability of a CEO being fired, P(B) be the probability of a "good" performance rating, P(B I A) be the likelihood of a "good" performance rating given that the CEO was fired, and P(A I B) be the likelihood of the CEO being fired given a "good" performance rating.)

选项：

A.

1.5%

B.

2.5%

C.

3.0%

解释：

C is correct. With Bayes' formula, the probability of the CEO being fired given a "good" rating is：

P(A∣B)=P(B∣A)P(B)P(A)P(A|B) = \frac{{P(B|A)}}{{P(B)}}P(A)

where

P(A) = 0.05 = probability of the CEO being fired

P(B) = 0.50 = probability of a "good" rating

P(B | A) = 0.30 = probability of a "good" rating given that the CEO is fired

With these estimates, the probability of the CEO being fired given a "good" rating is：

P(A∣B)=P(B∣A)P(B)P(A)=0.30.5×0.05=0.03P(A|B) = \frac{{P(B|A)}}{{P(B)}}P(A) = \frac{{0.3}}{{0.5}} \times 0.05 = 0.03

Although 5% of all CEOs are fired, the probability of being fired given a "good" performance rating is 3%.

知识点：Probability Concepts-Bayes' Formula

30% of all CEOs who were fired had "good" performance.

这句话读不懂是P（B|A）还是P（A|B）

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1 个答案

星星_品职助教 · 2023年08月08日

同学你好，

这句话的意思是：在被解雇的CEO中，有30%是good performance。也就是CEO被解雇是前提条件。

写成概率形式就是P(good|CEO fired）=30%，换成字母就是P(B|A)

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2022-06-23 20:10 1 · 回答

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