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claireteng · 2022年06月21日

请问这种题超纲吗？

  1. FRM I
  2. Quantitative

NO.PZ2020010301000005

问题如下：

Based on the probabilities in the plot below, what are the values of the following?

a. Pr(AC)Pr(A^C)

b. Pr(D|A∪B∪C)

c. Pr(A|A)

d. Pr(B|A)

e. Pr(C|A)

f. Pr(D|A)

g. Pr((A∪D)C)Pr({(A∪D)}^C)

h. Pr((AC⋂DC))Pr((A^C\bigcap D^C))

i. Are any of the four events pairwise independent?

解释：

a. 1 - Pr(A) = 100% - 30% = 70%

b. This value is Pr(D∩(A∪B∪C))/Pr(A∪B∪C). The total probability in the three areas A, B, and C is 73%. The overlap of D with these three is 9% + 8% + 7% = 24%, and so the conditional probability is 24%/73%= 33%.

c. This is trivially 100%.

d. Pr(B∩A) = 9%. The conditional probability is 9%/30% = 30%.

e. There is no overlap and so Pr(C∩A) = 0.

f. Pr(D∩A) = 9%. The conditional probability is 30%.

g. This is the total probability not in A or D. It is 1 – Pr(A∪D) = 1 - (Pr(A) + Pr(D) - Pr(A∩D)) = 100% - (30% + 36% - 9%) = 43%.

h. This area is the intersection of the space not in A with the space not in D. This area is the same as the area that is not in A or D, Pr((A∪D)C)Pr({(A\cup D)}^C) and so 43%.

i. The four regions have probabilities A = 30%, B = 30%, C = 28% and D = 36%. The only region that satisfied the requirement that the joint probability is the product of the individual probabilities is A and B because Pr(A∩B) = 9% = Pr(A)Pr(B) = 30% * 30%.

请问这种题超纲吗？感觉好多符号讲义中没有
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2 个答案

品职答疑小助手雍 · 2022年06月22日

讲过条件概率和交集并集的概念，那结合运用起来就可以了。知识点的穿插结合运用可以组合出很多能用方法，也就有很多问题，不太可能把所有知识点都排列组合穷举讲解。

品职答疑小助手雍 · 2022年06月21日

同学你好，不超纲，总共这题总共只有3个符号吧，交集∩、并集∪、条件概率|

交集的符号∩讲义13页有符号显示，34页例题也有，条件概率的竖线讲义里有很多，老师板书里应该也会提到。

这些符号高一时候学集合的子交并补时候都应该有学的，实在觉得陌生就只能百度了。

claireteng · 2022年06月22日

老师并没有讲有交集或并集情况下的条件概率吧

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