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卓娅 · 2023年05月26日

第二步不太明白

  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.

答案解析第二步不明白

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1 个答案

星星_品职助教 · 2023年05月26日

同学你好，

第二步是根据概率计算方差的过程。

根据第一步算出来的均值，把三个数字和各自对应的概率逐个代入下面的公式中即可得到方差。此后直接开根号就可以得到题目要求计算的标准差（答案解析第三步）


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NO.PZ2017092702000073 问题如下 The probability stribution for a company’s sales is:The stanrviation of sales is closest to: A.$9.81 million. B.$12.20 million. C.$32.40 million. A is correct. The analyst must first calculate expectesales 0.05 × $70 + 0.70 × $40 + 0.25 × $25 = $3.50 million + $28.00 million + $6.25 million = $37.75 million. After calculating expectesales, we ccalculate the varianof 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 stanrviation of sales is thus σ = ($96.18)1/2 = $9.81 million. 1

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