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ronica44 · 2023年01月23日

用Baye‘s rules来计算连续两年高投资回报前提下投资经理是投资明星的概率

Question:

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


Answer :

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%. Combining these values, 20% * 20% * 10% 0.625%

= 64%. This is a large increase from the 30% chance after one year.

我对公式没有疑问,但不理解两个地方:第一,答案中20%和5%是怎么得到的?第二,为啥(low, high)不是其中一个情形

1 个答案
已采纳答案

DD仔_品职助教 · 2023年01月25日

嗨,努力学习的PZer你好:


同学你好,

1,20%和5%是题目给出的已知条件,题目已知star一年高收益的可能性是20%,普通一年高收益的可能性是5%,我把完整的题目在这里截图一下:

2,(low, high)也是情况之一,这里答案我也不知道为啥没有提到。。。但是提不提到他都无所谓,因为我们只考虑4种情况里的连续两年都高也就是(high,high的情况)

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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