开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

这是名字 · 2025年06月14日

basic statistics练习题3

  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.


这道题为什么要先normalized概率再做呢？这个normalized的过程是怎么做的呢？


添加评论
1 个答案

李坏_品职助教 · 2025年06月14日

嗨，从没放弃的小努力你好：


因为原始的数据算出来：

这里non normalized就是根据题目原始数据求出来的，加起来不是100%的权重。所谓的normalized就是等比例放大，先求出non normalized加起来是49.89%， 这个是unconditional的，题目要求的是conditional，条件概率，所谓条件概率就是要求每个子集加起来是100%. 100 / 49.89 = 2.004.


说明我们需要把上面每一行的数字都乘以2.004，比如5.87% * 2.004 = 11.77%

----------------------------------------------
就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

  • 1

    回答

  • 0

    关注

  • 3

    浏览
相关问题

NO.PZ2020010304000016问题如下 Suppose ththe annuprofit of two firms, one incumbent (Big Firm, X1) anthe other a startup (Small Firm, X2), cscribewith the following probability matrix:Whare the contionexpecteprofit ancontionstanrviation of the profit of Big Firm when Small Firm either hno profit or loses money (X2 ≤ 0)?A.3.01; 30.52B.3.01; 931C.1.03; 30.521.03; 931.25 We neeto compute the contionstribution given X2 ≤ 0. The relevant rows of the probability matrix areThe contionstribution cconstructesumming across rows anthen normalizing to sum to unity. The non-normalizesum anthe normalizeversion areFinally, the contionexpectation is E[X1|X2 ≤0] = Σx1Pr(X1 = x1|X2 ≤0) = US3.01M. The contionexpectation squareis E[X1^2|X2 ≤0]=940.31, ansothe contionvarianis V[X1] = E[X1^2] - E[X1]^2 =940.31-3.01^2=931.25anthe contionstanrviation is US30.52M.为什么这题的条件概率可以直接把符合条件的两个概率相加，然后算出来的权重就可以当成概率求期望？不用拿联合除以边缘再算吗

2025-02-25 15:14 1 · 回答

NO.PZ2020010304000016问题如下Suppose ththe annuprofit of two firms, one incumbent (Big Firm, X1) anthe other a startup (Small Firm, X2), cscribewith the following probability matrix:Whare the contionexpecteprofit ancontionstanrviation of the profit of Big Firm when Small Firm either hno profit or loses money (X2 ≤ 0)?A.3.01; 30.52B.3.01; 931C.1.03; 30.521.03; 931.25 We neeto compute the contionstribution given X2 ≤ 0. The relevant rows of the probability matrix areThe contionstribution cconstructesumming across rows anthen normalizing to sum to unity. The non-normalizesum anthe normalizeversion areFinally, the contionexpectation is E[X1|X2 ≤0] = Σx1Pr(X1 = x1|X2 ≤0) = US3.01M. The contionexpectation squareis E[X1^2|X2 ≤0]=940.31, ansothe contionvarianis V[X1] = E[X1^2] - E[X1]^2 =940.31-3.01^2=931.25anthe contionstanrviation is US30.52M.算方差时，那个940.31怎么来的，没看懂，x1取多少啊

2025-02-15 16:12 1 · 回答

NO.PZ2020010304000016问题如下Suppose ththe annuprofit of two firms, one incumbent (Big Firm, X1) anthe other a startup (Small Firm, X2), cscribewith the following probability matrix:Whare the contionexpecteprofit ancontionstanrviation of the profit of Big Firm when Small Firm either hno profit or loses money (X2 ≤ 0)?A.3.01; 30.52B.3.01; 931C.1.03; 30.521.03; 931.25 We neeto compute the contionstribution given X2 ≤ 0. The relevant rows of the probability matrix areThe contionstribution cconstructesumming across rows anthen normalizing to sum to unity. The non-normalizesum anthe normalizeversion areFinally, the contionexpectation is E[X1|X2 ≤0] = Σx1Pr(X1 = x1|X2 ≤0) = US3.01M. The contionexpectation squareis E[X1^2|X2 ≤0]=940.31, ansothe contionvarianis V[X1] = E[X1^2] - E[X1]^2 =940.31-3.01^2=931.25anthe contionstanrviation is US30.52M.The contionexpectation squareis E[X1^2|X2 ≤0]=940.31, ansothe contionvarianis V[X1] = E[X1^2] - E[X1]^2 =940.31-3.01^2=931.25。然后有了第一问的期望减去每个数值，然后用到标准化之后的概率，不就可以算出方差了吗

2025-02-15 11:29 2 · 回答

NO.PZ2020010304000016 问题如下 Suppose ththe annuprofit of two firms, one incumbent (Big Firm, X1) anthe other a startup (Small Firm, X2), cscribewith the following probability matrix:Whare the contionexpecteprofit ancontionstanrviation of the profit of Big Firm when Small Firm either hno profit or loses money (X2 ≤ 0)? A.3.01; 30.52 B.3.01; 931 C.1.03; 30.52 1.03; 931.25 We neeto compute the contionstribution given X2 ≤ 0. The relevant rows of the probability matrix areThe contionstribution cconstructesumming across rows anthen normalizing to sum to unity. The non-normalizesum anthe normalizeversion areFinally, the contionexpectation is E[X1|X2 ≤0] = Σx1Pr(X1 = x1|X2 ≤0) = US3.01M. The contionexpectation squareis E[X1^2|X2 ≤0]=940.31, ansothe contionvarianis V[X1] = E[X1^2] - E[X1]^2 =940.31-3.01^2=931.25anthe contionstanrviation is US30.52M. 如题，我这样计算出的答案S30.43

2024-03-11 17:13 1 · 回答