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Jy_L · 2020年02月21日

问一道题: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.

为什么最后求方差的时候,为什么没有除以n

2 个答案

星星_品职助教 · 2020年09月16日

@rabbit 如果给了权重,要求计算expected value,就用加权平均。没给权重,只给样本要求计算样本标准差,就用n-1。

后者也不用套用公式,直接按计算器就可以。

星星_品职助教 · 2020年02月21日

同学你好,

这道题是加权平均的形式。不同的sales对应着不同的权重。

如果除以n的话相当于权重都是1/n了,与题干不符

rabbit · 2020年09月16日

老师,那如果遇到样本,书上的公式是除以N-1 。那同样用加权平均计算吗?

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