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小悟空 · 2020年05月26日

问一道题：NO.PZ2017092702000073

  1. CFA I
  2. Quantitative

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.

老师，这道题我算了每一个Expect return 3.5,28,6.25


求variance时，为什么不是这样子算啊？


0.05（70-3.5）²+0.7（40-28）²+0.25（25-6.25）²=最后答案

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星星_品职助教 · 2020年05月26日

同学你好，

均值只有一个，算法是用概率做为权重的加权平均，对于本题而言，均值的算法是0.05 × 70 + 0.70 × 40 + 0.25 × 25 = 3.50 。只有这一个均值，代入方差公式的时候代入的也是3.5。是不存在单独按照概率逐个计算出多个均值的方法的。

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