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🌊Yuri🌊 · 2022年11月30日

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

请问题干中已经说明了两者是independence。为什么还要用乘法法则?乘法法则的概念不是算的两个事件同时发生的概率吗?都说明了independence那不是怎么算都是为0的吗?

1 个答案

星星_品职助教 · 2022年11月30日

同学你好,

Exclusive对应的结论为P(AB)=0,而independence对应的结论为P(AB)=P(A)×P(B)

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