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早早 · 2022年11月13日

老师,可以帮忙解析一下这道题,对应的是哪个知识点?

The conditional expected value of a random variable is best described as the:

  1. expected value of a random variable given an event or scenario.
  2. probability-weighted average of the possible outcomes of the random variable.
  3. weighted average of the probabilities of an event given all possible scenarios.


Solution

A is correct. The conditional expected value of a random variable is the expected value of a random variable given an event or scenario.

B is incorrect because an expected value (not a conditional expected value) is defined as the probability-weighted average of the possible outcomes of the random variable.

C is incorrect because an expected value is not a probability. This answer defines the total probability rule, which is the weighted average of the probabilities of an event given all possible scenarios.

Probability Concepts Learning Outcome

  1. Explain the use of conditional expectation in investment applications



1 个答案

星星_品职助教 · 2022年11月14日

同学你好,

这是条件期望的考点。条件期望即在一定条件下求出来的期望值,也就是A选项所描述的,在一个特定条件(环境)下求出来的随机变量的期望值。

B选项是随机变量的加权平均,其中权重为概率。这是普通的期望值的定义,没有强调在一定的条件下。

C选项是所有概率的加权平均,这是全概率的定义,不是期望的定义。

这个概念和考点都不是很重要,把这道题了解一下就可以。

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