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
