开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

lion · 2022年04月26日

如何画图

  1. FRM I
  2. Quantitative

NO.PZ2020010301000006

问题如下：

Suppose that 10% of fund managers are superstars. Superstars have a 20% chance of beating their benchmark by more than 5% each year(high return), whereas normal fund managers have only a 5% chance of beating their benchmark by more than 5%.

Continue the application of Bayes’ rule to compute the probability that a manager is a superstar after observing two years of “high” returns.

解释：

Consider the three scenarios: (High, High), (High, Low) and (Low, Low). We are interested in Pr (Star|High, High) using Bayes’ rule, this is equal to

Pr(High, High|Star)Pr(Star) /Pr(High, High).

Stars produce high returns in 20% of years, and so Pr(High, High|Star) = 20% * 20% Pr (Star) is still 10%.

Finally, we need to compute Pr (High, High), which is Pr(High, High|Star) Pr(Star) + Pr(High, High|Normal)Pr(Normal).

This value is 20% * 20% * 10% + 5% * 5% * 90% = 0.625%. Combing these values,

20% * 20% * 10%/0.625%=64%

This is a large increase from the 30% chance after one year.

本题如何画图，就是辅助做题图

添加评论
1 个答案

品职答疑小助手雍 · 2022年04月26日

同学你好，我觉得画图反而不如把情况列清楚更看得清晰。

因为题目给的前提是发现了一个人连续两年高收益，star连续两年高收益的概率是20%*20%=4%，普通人连续两年高收益的概率是5%*5%=0.25%，然后10%的人是star，90%的是普通，所以随意一个人连续高收益的概率就是4%*10%+0.25%*90%=0.625%。

其中这人是star的概率就是4%*10%=0.4%，

现在已知连续高收益的话，star的概率就是0.4/0.625

  • 1

    回答

  • 0

    关注

  • 362

    浏览
相关问题

NO.PZ2020010301000006问题如下Suppose th10% of funmanagers are superstars. Superstars have a 20% chanof beating their benchmark more th5% eayear(high return), wherenormfunmanagers have only a 5% chanof beating their benchmark more th5%.Continue the application of Bayes’ rule to compute the probability tha manager is a superstafter observing two years of “high” returns. Consir the three scenarios: (High, High), (High, Low) an(Low, Low). We are interestein Pr (Star|High, High) using Bayes’ rule, this is equtoPr(High, High|Star)Pr(Star) /Pr(High, High).Stars prohigh returns in 20% of years, anso Pr(High, High|Star) = 20% * 20% Pr (Star) is still 10%. Finally, we neeto compute Pr (High, High), whiis Pr(High, High|Star) Pr(Star) + Pr(High, High|Normal)Pr(Normal). This value is 20% * 20% * 10% + 5% * 5% * 90% = 0.625%. Combing these values,20% * 20% * 10%/0.625%=64% This is a large increase from the 30% chanafter one year.1、老师好，“Pr(High, High|Star) ”这里的逗号（，）代表什么意思？是（1）以high｜star为条件的high的概率？还是（2）以star为条件，第一年high同时第二年high的概率？2、“Pr(High, High|Star) = 20% * 20% Pr (Star) is still 10%”如果是（2）的意思，那么“Pr(High, High|Star)”不应该是（20%*20%*10%）/10%吗？

2024-07-14 21:24 3 · 回答

NO.PZ2020010301000006 问题如下 Suppose th10% of funmanagers are superstars. Superstars have a 20% chanof beating their benchmark more th5% eayear(high return), wherenormfunmanagers have only a 5% chanof beating their benchmark more th5%.Continue the application of Bayes’ rule to compute the probability tha manager is a superstafter observing two years of “high” returns. Consir the three scenarios: (High, High), (High, Low) an(Low, Low). We are interestein Pr (Star|High, High) using Bayes’ rule, this is equtoPr(High, High|Star)Pr(Star) /Pr(High, High).Stars prohigh returns in 20% of years, anso Pr(High, High|Star) = 20% * 20% Pr (Star) is still 10%. Finally, we neeto compute Pr (High, High), whiis Pr(High, High|Star) Pr(Star) + Pr(High, High|Normal)Pr(Normal). This value is 20% * 20% * 10% + 5% * 5% * 90% = 0.625%. Combing these values,20% * 20% * 10%/0.625%=64% This is a large increase from the 30% chanafter one year. ‘Finally, we neeto compute Pr (High, High), whiis Pr(High, High|Star) Pr(Star) + Pr(High, High|Normal)Pr(Normal).’

2024-01-01 17:29 3 · 回答

NO.PZ2020010301000006 问题如下 Suppose th10% of funmanagers are superstars. Superstars have a 20% chanof beating their benchmark more th5% eayear(high return), wherenormfunmanagers have only a 5% chanof beating their benchmark more th5%.Continue the application of Bayes’ rule to compute the probability tha manager is a superstafter observing two years of “high” returns. Consir the three scenarios: (High, High), (High, Low) an(Low, Low). We are interestein Pr (Star|High, High) using Bayes’ rule, this is equtoPr(High, High|Star)Pr(Star) /Pr(High, High).Stars prohigh returns in 20% of years, anso Pr(High, High|Star) = 20% * 20% Pr (Star) is still 10%. Finally, we neeto compute Pr (High, High), whiis Pr(High, High|Star) Pr(Star) + Pr(High, High|Normal)Pr(Normal). This value is 20% * 20% * 10% + 5% * 5% * 90% = 0.625%. Combing these values,20% * 20% * 10%/0.625%=64% This is a large increase from the 30% chanafter one year. 连续两年的概率是20%*20%，5%*5%，不是20%+20%，5%+5%，为什么是相乘，不是相加，怎么理解？

2023-12-17 12:10 1 · 回答

NO.PZ2020010301000006 问题如下 Suppose th10% of funmanagers are superstars. Superstars have a 20% chanof beating their benchmark more th5% eayear(high return), wherenormfunmanagers have only a 5% chanof beating their benchmark more th5%.Continue the application of Bayes’ rule to compute the probability tha manager is a superstafter observing two years of “high” returns. Consir the three scenarios: (High, High), (High, Low) an(Low, Low). We are interestein Pr (Star|High, High) using Bayes’ rule, this is equtoPr(High, High|Star)Pr(Star) /Pr(High, High).Stars prohigh returns in 20% of years, anso Pr(High, High|Star) = 20% * 20% Pr (Star) is still 10%. Finally, we neeto compute Pr (High, High), whiis Pr(High, High|Star) Pr(Star) + Pr(High, High|Normal)Pr(Normal). This value is 20% * 20% * 10% + 5% * 5% * 90% = 0.625%. Combing these values,20% * 20% * 10%/0.625%=64% This is a large increase from the 30% chanafter one year. 这个题目的提问内容意思我没有完全看懂，另外请老师用中文，并用图示法讲解一下，谢谢！

2023-06-08 13:07 1 · 回答