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珈柠 · 2024年08月02日

CFA|

NO.PZ2022123001000088

问题如下:

There are three fat-tailed samples.The followings are their standard error of the sample mean and sample variance. Which sampling distribution of the sample mean has fatter tails?

选项:

Standard error of the sample mean
Sample variance

A.

5
100

B.

2
64

C.

3
81

解释:


With the knowing standard deviation and standard error, the sample size(n) is:

nA=4; nB=16; nC=9

According to the central limit theorem, a sampling distribution of the sample mean will be approximately normal only if the sample size n is large. As n increase, the sampling distribution of the the sample mean will has less fat tails. So A with a smallest size is correct.

请问这道题怎么理解?

1 个答案
已采纳答案

品职助教_七七 · 2024年08月02日

嗨,努力学习的PZer你好:


这道题考察 n越大,sample mean的分布就和正态分布越像。如果n大于30,则sample mean的分布就趋近于正态了。

根据标准误的公式反算n后,可以发现C选项的n最大。也就最像正态分布。A选项的n最小,也就最不像正态分布。

由于这三个分布都是肥尾分布,所以最不像正态分布的就是尾巴最肥的,也就是A选项。

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