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赵磊fantasy · 2020年02月16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.

求一个详细的解题步骤,没看明白

1 个答案

品职答疑小助手雍 · 2020年02月17日

同学你好,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。

Roxanne_104 · 2020年02月17日

请问为什么将这4个数等比例扩充到总概率等于100%就是条件概率?

品职答疑小助手雍 · 2020年02月17日

因为条件概率就是这四个数的合集作为条件的概率啊,在这个条件(这四个数作为全集的条件)下,这四个数所占的概率。

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