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April · 2021年05月18日

老师,请问expected sales在各组概率和sales相乘并相加后,为什么不除以3呢?

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.

老师,请问expected sales在各组概率和sales相乘并相加后,为什么不除以3呢?

1 个答案
已采纳答案

星星_品职助教 · 2021年05月18日

同学你好,

“除以3”相当于在计算算术平均,这种算法应该是(70+40+25)/3。

如果把式子写开,就是1/3×70+1/3×40+1/3×25。可以看出,这种方式实际上是相当于一个特殊的加权平均,此时权重为相等的1/3.

而这道题的权重已经给出了,就是三个概率。

所以计算加权平均的时候,就直接用概率做权重乘以对应的金额就可以了,即0.05 × 70 + 0.70 × 40 + 0.25 × 25。算出来就是平均值,就也不用再除以3了。

计算expected value时用的都是这种概率做权重的加权平均方法。

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