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轨迹 · 2020年10月11日

问一道题:NO.PZ2017092702000064 [ CFA I ]

问题如下:

After estimating the probability that an investment manager will exceed his benchmark return in each of the next two quarters, an analyst wants to forecast the probability that the investment manager will exceed his benchmark return over the two-quarter period in total. Assuming that each quarter’s performance is independent of the other, which probability rule should the analyst select?

选项:

A.

Addition rule

B.

Multiplication rule

C.

Total probability rule

解释:

B is correct.

Because the events are independent, the multiplication rule is most appropriate for forecasting their joint probability. The multiplication rule for independent events states that the joint probability of both A and B occurring is P(AB) = P(A)P(B).

两个均超过应该是“both”, 而这里说“in total”可以理解为一个月没超过而另一个月超过了很多时,也可以达到两个月总共“in total”超过了。所以应该用全概率rules,不是吗?
1 个答案

星星_品职助教 · 2020年10月11日

同学你好,

首先全概率公式的应用是以概率为权重,求加权平均,在这道题里不适用。

其次看这道题题干结构,这里面有一个前后文的对应关系。

前面说了“estimating the probability that an investment manager will exceed his benchmark return in each of the next two quarters”,即这个基金经理估计了两个概率,这两个概率是未来两个季度里,每个季度各自(in each)超过benchmark的概率。

所以下文是在这个基础上,根据这两个概率来预测(forecast)两个季度都超过benchmark的概率,并假设独立。所以这是一个乘法法则的应用。

------------

协会是不会在这种定语类的词汇上做文章来考英语的,不用去死扣某个定语,这样思路就偏了。

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