为什么算期望的时候不需要乘以第一支的概率？

NO.PZ2022123001000047

问题如下：

An analyst gathered the following information: the probability of economy prosperity is 75%, the probability of economy recession is 25%. For a company, when the economy is prosperity, there is 10% of probability that its EPS is $2.0 and 90% of probability that the EPS is $4.0. However, when the economy is recession, there is 25% of probability that the EPS is $2.0 and 75% of probability that the EPS is $4.0. What is the variance of this company’s EPS, when the economy is recession?

选项：

3.55

1.25

0.75

解释：

When the economy recession:

E(EPS) = 25% * 2 + 75% *4 = 3.5, Var(EPS) = 25% * (2-3.5)²+ 75% * (4-3.5)² = 0.75

经济上行下行的概率作为第一支为什么计算的时候不考虑，而只考虑第二支的概率呢？

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1 个答案

品职助教_七七 · 2025年04月30日

嗨，从没放弃的小努力你好：

“第一支”对应的是经济是否为recession的概率。由于本题最后已经说明了此时就是recession（when the economy is recession），所以“第一支”已经是既成事实了，不再有“概率”的情况。或者说recession的概率此时就是100%。

所以不需要代入概率来计算第一支。

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NO.PZ2022123001000047 问题如下 analyst gatherethe following information: theprobability of economy prosperity is 75%, the probability of economy recessionis 25%. For a company, when the economy is prosperity, there is 10% ofprobability thits EPS is $2.0 an90% of probability ththe EPS is $4.0.However, when the economy is recession, there is 25% of probability ththe EPSis $2.0 an75% of probability ththe EPS is $4.0. Whis the varianofthis company’s EPS, when the economy is recession? A.3.55 B.1.25 C.0.75 When the economyrecession:E(EPS)= 25% * 2 + 75% *4 = 3.5, Var(EPS) = 25% * (2-3.5)2 + 75% * (4-3.5)2= 0.75 计算EPS的方差，用加权平均来算，为什么不能像算portfolio的方差一样权重去平方

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