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Infinite · 2020年02月13日

问一道题:NO.PZ2020010304000015

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:

If an investor owned 20% of Big Firm and 80% of Small Firm, what are the expected profits of the investor and the standard deviation of the investor’s profits?

选项:

A.

4.18; 8.39

B.

4.18; 70.39

C.

2.18; 8.39

D.

2.18; 70.39

解释:

The expected profits are E[P] = 20% * E[X1] + 80% * E[X2] = 4.18.

The variance of the portfolio is (20%)^2*Var[X1] + (80%)^2*Var[X2] + 2(20%)(80%)Cov[X1, X2]

This value is 0.04 * 1534.36 + 0.64 * 2.41 + 2 * 0.16 * 23.37 = 70.39, and so the standard deviation is USD 8.39M.

能否麻烦把这道题带数字版的解答写上来,var(small) var(big) cov(small, big) ,谢谢!

1 个答案

品职答疑小助手雍 · 2020年02月14日

同学你好,cov的话:这个前一题2020010304000014求过的,cov(x1,x2)=E(x1*x2)+E(x1)*E(x2)

E(x1*x2)等于表格里每个格子的概率*概率对应的x1*x2,拿第一格举例就是1.97%*1M*(-50M),最后加总等于43.22

E(x1)和E(x2)都好求,这三个数套那个cov的公式就行了。


var的话以var(small )为例:variance(small)=E(small的平方)-[E(small)的平方]来算,等于(第一列的累计概率*负1的平方+第二列的累计概率*0的平方+第三列的累计概率*2的平方+第四列的累计概率*4的平方)-(第一列的累计概率*负1+第二列的累计概率*0+第三列的累计概率*2+第四列的累计概率*4)的平方=3.97-1.56=2.41