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下钱的雨 · 2018年08月21日

标准正态分布的公式问题

There are two steps in

standardizing

a random variable

X

: Subtract the mean of

X

from

X,

then divide that result by the standard deviation of

X

. If we have a list of observations on a normal random variable,

X,

we subtract the mean from each observation to get a list of deviations from the mean, then divide each deviation by the standard deviation. The result is the standard normal random variable,

Z.

(

Z

is the conventional symbol for a standard normal random variable.) If we have

X

~

N

(μ,σ

2

) (read “

X

follows the normal distribution with parameters μ and σ

2

”), we standardize it using the formula

(Institute 548)

Institute, CFA. 2018 CFA Program Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. CFA Institute, 07/2017. VitalBook file.


Equation (4) 

Z = (X – μ)/σ  

(Institute 548)

Institute, CFA. 2018 CFA Program Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. CFA Institute, 07/2017. VitalBook file.



我的问题是:为什么把一个正态分布的取值减去均值再除以标准差就是标准化了?

1 个答案

菲菲_品职助教 · 2018年08月21日

同学你好,这个不在考试要求内,只要记住公式就好。这个公式的由来牵扯到积分问题,下图是一个简单的解释,如果你实在感兴趣,可以自行上网研究。

 

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