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Pavel Korchagin · 2023年06月16日

为什么不用最后-0.01呢？

  1. CFA I
  2. Quantitative

NO.PZ2017092702000091

问题如下：

The cumulative distribution function for a discrete random variable is shown in the following table.

The probability that X will take on a value of either 2 or 4 is closest to:

选项：

A.

0.20.

B.

0.35.

C.

0.85.

解释：

A is correct.

The probability that X will take on a value of 4 or less is: F(4) = P(X ≤ 4) = p(1) + p(2) + p(3) + p(4) = 0.60. The probability that X will take on a value of 3 or less is: F(3) = P(X ≤ 3) = p(1) + p(2) + p(3) = 0.50. So, the probability that X will take on a value of 4 is: F(4) – F(3) = p(4) = 0.10. The probability of X = 2 can be found using the same logic: F(2) – F(1) = p(2) = 0.25 – 0.15 = 0.10. The probability of X taking on a value of 2 or 4 is: p(2) + p(4) = 0.10 + 0.10 = 0.20.

为什么不是0.1+0.1-0.01=0.19

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2 个答案

星星_品职助教 · 2023年06月16日

@libaicun

1）加法法则为：P(A or B)=P(A)+P(B)-P(AB)，其中P(AB)为A和B共同发生的概率。

2）由于本题的两个事件分别为X=2和X=4，这两个事件不能同时发生（互斥事件），所以P(AB)=0，而不是两者的乘积0.01。

3）此时加法法则简化为P(A or B)=P(A)+P(B)，也就是P(2 or 4)=P(2) + P(4) 。

星星_品职助教 · 2023年06月16日

同学你好，

请补充说明一下 0.01的来源，及认为需要减掉它的逻辑。

Pavel Korchagin · 2023年06月16日

就是前面学的加法法则p(a or b)=pa+pb–pa＊pb

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NO.PZ2017092702000091 问题如下 The cumulative stribution function for a screte ranm variable is shown in the following table. The probability thX will take on a value of either 2 or 4 is closest to: A.0.20. B.0.35. C.0.85. A is correct. The probability thX will take on a value of 4 or less is: F(4) = P(X ≤ 4) = p(1) + p(2) + p(3) + p(4) = 0.60. The probability thX will take on a value of 3 or less is: F(3) = P(X ≤ 3) = p(1) + p(2) + p(3) = 0.50. So, the probability thX will take on a value of 4 is: F(4) – F(3) = p(4) = 0.10. The probability of X = 2 cfounusing the same logiF(2) – F(1) = p(2) = 0.25 – 0.15 = 0.10. The probability of X taking on a value of 2 or 4 is: p(2) + p(4) = 0.10 + 0.10 = 0.20. 老师这道题里为什么要求x小于等于4的概率和x小于等于2的概率，直接用x=4和2的概率相加不行吗

2023-03-16 18:17 1 · 回答

NO.PZ2017092702000091问题如下The cumulative stribution function for a screte ranm variable is shown in the following table. The probability thX will take on a value of either 2 or 4 is closest to:A.0.20.B.0.35.C.0.85.A is correct. The probability thX will take on a value of 4 or less is: F(4) = P(X ≤ 4) = p(1) + p(2) + p(3) + p(4) = 0.60. The probability thX will take on a value of 3 or less is: F(3) = P(X ≤ 3) = p(1) + p(2) + p(3) = 0.50. So, the probability thX will take on a value of 4 is: F(4) – F(3) = p(4) = 0.10. The probability of X = 2 cfounusing the same logiF(2) – F(1) = p(2) = 0.25 – 0.15 = 0.10. The probability of X taking on a value of 2 or 4 is: p(2) + p(4) = 0.10 + 0.10 = 0.20.如题。。。。。。。。

2023-02-06 13:42 1 · 回答

The probability that X will take on a value of either 2 or 4 is closest to 是同时取2和4的概率的意思？

2020-06-01 20:15 1 · 回答

    老师，这道题的表格 看不懂是什么意思，麻烦解答，谢谢！

2019-09-12 19:35 1 · 回答