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涵 · 2024年03月11日

你好，请问标准化后，计算SD，是否可用W1（X1-u）平方+...+W3（X3-u）平方来求Variance，然后再开方呢

  1. FRM I
  2. Quantitative

NO.PZ2020010304000016

问题如下：

Suppose that the annual profit of two firms, one an incumbent (Big Firm, X1) and the other a startup (Small Firm, X2), can be described with the following probability matrix:

What are the conditional expected profit and conditional standard deviation of the profit of Big Firm when Small Firm either has no profit or loses money (X2 ≤ 0)?

选项：

A.

3.01; 30.52

B.

3.01; 931

C.

1.03; 30.52

D.

1.03; 931.25

解释：

We need to compute the conditional distribution given X2 ≤ 0. The relevant rows of the probability matrix are

The conditional distribution can be constructed by summing across rows and then normalizing to sum to unity. The non-normalized sum and the normalized version are

Finally, the conditional expectation is E[X1|X2 ≤0] = Σx1Pr(X1 = x1|X2 ≤0) = USD 3.01M.

The conditional expectation squared is E[X1^2|X2 ≤0]=940.31, and so

the conditional variance is V[X1] = E[X1^2] - E[X1]^2 =940.31-3.01^2=931.25

and the conditional standard deviation is USD 30.52M.

如题，我这样计算出的答案SD=30.43

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1 个答案

李坏_品职助教 · 2024年03月11日

嗨，从没放弃的小努力你好：


也可以，本题中的conditional variance是940.31-3.01^2 = 931.25， 开根号就是30.52。


如果按照你的想法：

conditional variance = 11.77%*(-50-3.01)^2 + 54.98%*(0-3.01)^2 + 27.06%*(10-3.01)^2 + 6.19%*(100-3.01)^2 = 931.24, 开根号之后是30.52.


你可能是因为四舍五入的问题，和答案略有差异。

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