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勇往直前 · 2022年04月02日

完全看不懂怎么算的,又不能画图,转晕了,请老师帮忙,否则得放弃这块了。。。

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(AB)=P(BA)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(AB)=P(BA)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

完全看不懂怎么算的,又不能画图,转晕了,请老师帮忙,否则得放弃这块了。。。

2 个答案
已采纳答案

星星_品职助教 · 2022年04月02日

同学你好,

公式法是很简单的,有固定的流程。

①首先记忆公式,贝叶斯题目的公式和乘法法则的形式是一样的。乘法法则公式为P(AB)=P(A|B)×P(B)=P(B|A)×P(A)。把上述连等式的后两项重新组合一下,就可以得到P(A|B)=P(B|A) / P(B) × P(A)。

②在实际题目中,都不用去特意设定谁是A谁是B,直接按照最后的问法写出来就可以。本题问的是 the probability that a CEO will be fired given "good" performance,即P(CEO is fired | good rating),据此就直接可以写出公式为:

P(CEO is fired | good rating)=P(good rating | CEO is fired) / P(good rating) × P(CEO is fired)

③此后就从题干中找条件代数就行,公式右边的三项都直接给出了。

----------

在本题中,找到:

1)5% of all CEOs are fired,这就是P(CEO is fired)=5%;

2)50% of stocks have above-average returns or "good" performance,这就是P(good rating)=50%;

3)30% of all CEOs who were fired had "good" performance,这就是P(good rating | CEO is fired) =30%;

代入公式,直接得到 30% / 50% × 5%=3%

-------

只要掌握了上述思维,贝叶斯的公式法就是纯代数字的题目。

Avalon · 2022年05月05日

谢谢老师,讲得非常好!

星星_品职助教 · 2022年05月06日

@鲤哩哩哩哩哩

学习加油~

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2023-08-07 14:34 1 · 回答

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2021-12-16 13:21 2 · 回答

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