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13995173783 · 2023年06月13日

mormalized怎么实现的

  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.

请老师解答一下，NONMORMALIZED（是什么意思？）怎么计算mormalized数据，谢谢！

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1 个答案

pzqa27 · 2023年06月14日

嗨，从没放弃的小努力你好：


同学你好，先把小于等于0的概率相加，得到第二个表的左半边，因为问的就是小公司亏钱或者不赚钱的条件概率，第二张图第一列那个non-normalized其实就是常规的概率，拿前两行举例5.87%和27.43%分别是1.97%+3.9%和3.93%+23.5%的结果。


然后normalize其实就是求条件概率，也就是把这4个数等比例扩充到总概率等于100%就行了，假设一个扩大系数X，（5.87%+27.43%+13.5%+3.09%）*X=100%，求出来X，然后把这4个数分别乘以X就得到右边那列normalized数据了。

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努力的时光都是限量版，加油！

13995173783 · 2023年06月14日

谢谢老师

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