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Amber Guo · 2022年08月16日

CFA I Mock

Which of the following most accurately describes how to standardize a random variable X?

A. Subtract the mean of X from X, and then divide that result by the standard deviation of the standard normal distribution.

B. Divide X by the difference between the standard deviation of X and the standard deviation of the standard normal distribution.

C. Subtract the mean of X from X, and then divide that result by the standard deviation of X.

Solution: C

There are two steps in standardizing a random variable X: Subtract the mean of X from X, and then divide that result by the standard deviation of X. This is represented by the following formula: Z = (X − μ)/σ.

求问老师为什么标准化不选A?这个不是正态分布的标准化吗?

1 个答案

星星_品职助教 · 2022年08月16日

同学你好,

A、B选项的描述都是“ the standard deviation of the standard normal distribution”。标准化公式中的分母并不是标准正态分布的标准差,标准正态分布的标准差永远等于1.

正确的描述应为the standard deviation of X,即随机变量自身的标准差,也就是公式中的σ。

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