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Allez😃Sea · 2020年03月30日

问一道题：NO.PZ2018062016000091

  1. CFA I
  2. Quantitative

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，为什么这题不可以用 x2-x1/b-a 来计算？

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星星_品职助教 · 2020年03月30日

同学你好，

首先P(x1 ≤X ≤x2) = (x2 –x1)/(b – a)是Continuous Uniform Distribution才有的性质，这道题为 discrete random variable，本身就不能用。

其次这道题并不是在求P(23 ≤X ≤25) ，而是求Y takes 23 or 25，这是典型的A or B问题，所以需要求出Y=23和Y=25的概率，然后进行相加。

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