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贺采🌻 · 2021年08月04日

不能用加法法则吗

  1. CFA I
  2. Quantitative

NO.PZ2018062016000091

问题如下：

Given a discrete random variable Y, the set of all the possible Y value is Y = {20,21,22,23,24,25}.

The estimated value of cumulative distribution function is in the table, what is the probability that Y takes 23 or 25?

选项：

A.

0.50

B.

0.45

C.

0.75

解释：

A is correct. 

F(23) = P(Y≤ 23) = p(20) + p(21) + p(22) + p(23) = 0.55. F(22) = P(Y≤ 22) = p(20) + p(21) + p(22) = 0.30. So p(23) = 0.55-0.30 = 0.25.

For the same reason, F(25) = 1.00, F(24) = 0.75, p(25) = 1.00-0.75 = 0.25.

The probability that Y takes 23 or 25 = p(23) + p(25) = 0.25+0.25 = 0.50

老师，这个取到23或25的概率不可以用加法法则吗（两个至少取到一个的概率） 就是(0.25+0.25)-0.25*0.25
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星星_品职助教 · 2021年08月04日

同学你好，

加法法则的公式为： P(A or B)=P(A)+P(B)-P(AB)，而你的列式为P(A or B)=P(A)+P(B)-P(A)×P(B).

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这道题用的是加法法则。由于Y取23，和Y取25这两个事件是互斥事件。所以可以得到它们共同发生的概率是0.

所以此时加法法则退化为 P(A or B）=P(A)+P(B)，就不存在后面的P(AB）了

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