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April004 · 2020年02月06日

问一道题：NO.PZ2020010304000013

  1. FRM I
  2. Quantitative

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 is the conditional distribution of Small Firm’s profits if Big Firm has a $100M profit year?

选项：

解释：

The conditional distribution is just the row corresponding to USD 100M normalized to sum to 1. The conditional is different from the marginal, which is another demonstration that the profits are not independent.

怎么算的？

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1 个答案

orange品职答疑助手 · 2020年02月06日

同学你好，因为这是求的条件分布，所以应该在Big firm X1 = 100M的条件下，再去算它的概率。所以应该把X1=100时，X2取各值的概率，同比例增大，使得新的四个概率之和为100% 。拿19.5%举例：

3.09%/(3.09%+6.58%+6.16%)=19.5%

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