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shuangzili · 2021年11月21日

其他错误选项是什么意思？

  1. CFA I
  2. Quantitative

NO.PZ2017092702000064

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).

基金经理估计了两个概率，这两个概率是未来两个季度里，每个季度各自超过benchmark的概率。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。所以需使用乘法法则

请问其他错误选项是什么意思，在哪些场景下应该选择另两个？ 谢谢
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1 个答案

星星_品职助教 · 2021年11月21日

同学你好，

A选项是加法法则，适用场景为求两件事情至少发生其中之一的概率;

B选项是乘法法则，适用场景为让第一件事先发生，在此基础上再让第二件事发生的概率。

C选项是全概率公式。适用场景往往是求均值（expected value）。例如给出股价未来变化的可能情况和相关概率，假设有70%可能达到100元，30%达到10元。则股价均值为70%×100+30%×10，这就是 total probability rule for expected value。

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