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wmm93512 · 2022年04月29日

为什么不能这么计算：

  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.

为什么不能这么计算：

E(x2)-E(x)2 =[0.05*702+0.7*402+0.25*252]-[(0.05*70)2+(0.7*40)2+(0.25*25)2]=685.93

σ(x) =685.931/2=26.19



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1 个答案

星星_品职助教 · 2022年04月29日

同学你好，

可以这样计算，结果是一样的。

问题中列式错在后半部分 [ E(X) ]^2 的计算，应该先算出E(X)，再平方。即先算出(0.05*70)+(0.7*40)+(0.25*25)=37.75，平方后为1,425.0625.

所以结果为1521.25-1,425.0625=96.1875，这是variance。再开根号后得到 standard deviation=9.8075

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