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熊冰清Blanche💫 · 2020年10月15日

问一道题:NO.PZ2020010304000012 [ FRM I ]

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:

Are the returns on the two firms independent?

解释:

They are independent if the joint is the product of the marginals.

Looking at the upper left cell, 6.77% * 6.70% is not equal to 1.97%, and so they are not.

这题怎么理解呢,没有太明白
1 个答案

袁园_品职助教 · 2020年10月16日

同学你好!

这道题就是让你判断独立事件。

答案中举了一个例子:

P (X1=-USD50M) = 1.97% + 3.9% + 0.8% + 0.1% = 6.77%

P (X2=-USD 1M) = 1.97% + 3.93% + 0.8% + 0% = 6.7%

P (X1=-USD50M, X2=-USD 1M) = 1.97% ≠  6.77% * 6.70%

即 P (X1=-USD50M, X2=-USD 1M) ≠ P (X1=-USD50M) * P (X2=-USD 1M)

所以他们不是互相独立的。

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