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Zili · 2023年08月19日

可以解释一下这题么?谢谢

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:

A.

3.55

B.

1.25

C.

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

可以解释一下这题么?谢谢

2 个答案

星星_品职助教 · 2023年08月20日

@Zili 所有用概率计算的方差都是加权平均,其中权重为概率。

星星_品职助教 · 2023年08月20日

同学你好,

1)此后提问请具体说明不懂的地方。

2)本题要求计算当经济确定为recession时的EPS方差。所以根据经济处于recession时的““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 ”,得到EPS的均值:

此后再根据方差的计算公式,代入求得的均值。即可求得方差:

Zili · 2023年08月20日

这里方差为什么是用加权平均的方式算的?