NO.PZ2015120601000008
问题如下：
An analyst developed two scenarios with respect to the recovery of $100,000 principal from defaulted loans:
The amount of the expected recovery is closest to:
选项：
A.
$36,400.
B.
$55,600.
C.
$63,600.
解释：
C is correct.
If Scenario 1 occurs, the expected recovery is 60% ($50,000) + 40% ($30,000) = $42,000, and if Scenario 2 occurs, the expected recovery is 90% ($80,000) + 10%($60,000) = $78,000.
Weighting by the probability of each scenario, the expected recovery is 40%($42,000) + 60%($78,000) = $63,600.
Alternatively, first calculating the probability of each amount occurring, the expected recovery is (40%)(60%)($50,000) + (40%)(40%)($30,000) + (60%)(90%)($80,000) + (60%)(10%)($60,000) = $63,600.
这道题考察加权平均计算均值（expected recovery），权重为概率。
①首先算出scenario 1中的加权平均值为50,000×60%+30,000×40%=42,000；
同理scenario 2中加权平均值为80,000×90%+60,000×10%=78,000.
②然后再将scenario1 &2做加权平均，
42,000×40%+78,000×60%=63,600，选择C选项。
40%*60%*50000+40%*40%*30000+60%*90%*80000+60%*10%*60000 =12000+4800+43200+36000=96000
