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还是星宇好 · 2020年05月30日

问一道题: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.

老师这个题我想问一下,表里面应该指的是x_1,x_2的联合概率(同时发生的概率),怎么直接把联合概率P(x_1,x_2)直接当条件概率P(x_1| x_2)用呢?

臭儿 · 2020年06月12日

请问:1.97%不是X1,x2的联合概率f(-50m,-1m)么? 为什么这里理解是f(X1|X2)条件概率f(-50m|-1m)=1.97%呢? 能否解释一下这个概率分布表的意思?

1 个答案

袁园_品职助教 · 2020年06月01日

同学你好!

解释中的第一个表格只是照抄一边题目表格中的左半部分

第二张才是去求解条件概率,non-normalized 就是直接相加,normalized 才是条件概率,就是使总和为100%

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