问题如下：
2、Assume a new investment manager has just beaten the market for two consecutive years. According to Bayes' rule, what is the probability that this new investment manager is excellent?
选项：
A. 20%.
B. 30%.
C. 40%
D. 45%.
解释：
C is correct.
考点：Bayes' rule
解析：首先定义事件如下：
A1——manager is excellent
A2——manager is average
A3——manager is poor
O2——投资经理连续两年战胜市场
本题求的是P(A1|O2)。
题目已知P(A1)=0.2，P(A2)=0.5，P(A3)=0.3 。
P(O2|A1) =0.8*0.8 =0.64 ，P(O2|A2)=0.6*0.6 =0.36，P(O2|A3)=0.2*0.2 =0.04
P(O2A2)+P(O2A3) = P(O2|A1)*P(A1) +P(O2|A2)*P(A2) +P(O2|A3)*P(A3) =0.64*0.2+0.36*0.5+0.04*0.3=0.32
P(A1|O2) = P(A1O2) / P(O2)= 0.64*0.2/0.32 = 0.4
答案里的解析看不太懂，可以请老师画个贝叶斯图吗？谢谢
