以及怎么得出的标准化以后的概率呢？
问题如下图：
选项：
A. 
B. 
C. 
D. 
解释：
品职答疑小助手雍 · 2020年01月16日
同学你好，这题其实和标准化关系不大，只是一个条件概率的问题，先把小公司不赚和亏钱的情况的概率分布找出来，然后把这俩情况下大公司的概率累加。
然后在小公司不赚或亏钱的情况下（把这情况当做100%），把大公司前面累加的概率扩充成合计100%的条件概率。然后按公式求期望和方差就行了。
标准化本身是一个数据处理的过程，因为平时的数据可能是各种各样的分布的，标准化mapping成一个理论里有成熟公式的分布可以更方便建模。具体方法要看是什么分布了，拿标准正态分布举例就是（X-μ）/σ
YolandaQ · 2020年01月19日
谢谢解答，但我发现我表达有点问题，我想问的是那些百分比normalized的逻辑，我不应该说成标准化。这些概率并不是加起来100%，为什么不直接乘，而是要先换算成加起来100%的数字？这些概率加起来本来原本并不是穷尽100%的呀，说明不是exhaust的，让人认为题目还有其他可能的事件，换算完却成了一组exhaust的概率，不是很明白。
品职答疑小助手雍 · 2020年01月20日
这些概率本身是占总体的概率，现在求的是条件概率，也就是在小公司不赚或者亏钱这个情况下的概率，也就是相当于假定前提就是小公司不赚或者亏钱这个事件是100%发生的，所以这些概率应该要穷尽这个情况。
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
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. normalize好像讲义里都没提到
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. E[X1|X2 ≤0] = Σx1Pr(X1 = x1|X2 ≤0) = US3.01M根据公式算出来的是1.5050，是哪里有问题吗？
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.讲义sli 71关于contionexpectation的例题中，storeturn 三个概率加起来也是不到100。但是最后解contionexpectation时也是直接用题目中的概率。请问为什么这道题要Normalize？没搞懂，可以一下吗？
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. 本题考点为条件期望和条件标准差，涉及期望、标准差计算公式以及条件概率性质。计算步骤如下1、条件期望为 E[X1|X2 ≤0]= Σx1Pr(X1 = x1|X2 ≤0)= Σx1*[Pr(X1 = x1,X2 ≤0)/Pr(X2 ≤0)]，依次带入X1取4个概率的数值计算。2、条件标准差为E[X1^2|X2 ≤0]- E[X1|X2 ≤0]^2，其中E[X1^2|X2 ≤0]=Σx1^2*Pr(X1 = x1|X2 ≤0)=Σx1^2*[Pr(X1 = x1,X2 ≤0)/Pr(X2 ≤0)]；E[X1|X2 ≤0]^2为计算1的结果。想知道以上思路和计算过程是否正确；整个计算比较繁琐，容易出错，是否有更高效的计算方法？