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ZC调频 · 2024年04月07日

标准差为什么是二分之一的方差

  1. CFA I
  2. Quantitative

NO.PZ2017092702000073

问题如下：

The probability distribution for a company’s sales is:

The standard deviation of sales is closest to:

选项：

A.

$9.81 million.

B.

$12.20 million.

C.

$32.40 million.

解释：

A is correct.

The analyst must first calculate expected sales as 0.05 × $70 + 0.70 × $40 + 0.25 × $25 = $3.50 million + $28.00 million + $6.25 million = $37.75 million. After calculating expected sales, we can calculate the variance of sales: = σ2 (Sales) = P($70)[$70 – E(Sales)]2 + P($40)[$40 – E(Sales)]2 + P($25)[$25 – E(Sales)]2 = 0.05($70 – 37.75)2 + 0.70($40 – 37.75)2 + 0.25($25 – 37.75)2 = $52.00 million + $3.54 million + $40.64 million = $96.18 million. The standard deviation of sales is thus σ = ($96.18)1/2 = $9.81 million.

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品职助教_七七 · 2024年04月07日

嗨，努力学习的PZer你好：


答案解析中为方差的1/2次方，即标准差为方差开根号后取正值，不是方差的1/2.

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努力的时光都是限量版，加油！

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