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# 概率论快速学习04：概率公理 全概率 贝叶斯 事件独立性

加油! 大牛总是不断努力,你却更需要加倍努力.

# Written In The Font

数学和生活是技术之本, 有了数学,加上生活,才会开心.

今天继续概率论:

• 全概率

• 贝叶斯

• 事件独立性

# Content

The total probability

In the Set :

The law of total probability is the proposition that if  is a finite or countably infinitepartition of a sample space (in other words, a set of pairwise disjoint events whose union is the entire sample space) and each event  is measurable, then for any event  of the same probability space:

example:

A表示产品合格，B表示产品来自甲厂

Bayes

for some partition {Bj} of the event space, the event space is given or conceptualized in terms of P(Bj) and P(A|Bj). It is then useful to compute P(Ausing the law of total probability:

example:

An entomologist spots what might be a rare subspecies of beetle, due to the pattern on its back. In the rare subspecies, 98% have the pattern, or P(Pattern|Rare) = 98%. In the common subspecies, 5% have the pattern. The rare subspecies accounts for only 0.1% of the population. How likely is the beetle having the pattern to be rare, or what is P(Rare|Pattern)?

From the extended form of Bayes' theorem (since any beetle can be only rare or common),

One more example:

### Independence

###### Two events

Two events A and B are independent if and only if their joint probability equals the product of their probabilities:

• .

Why this defines independence is made clear by rewriting with conditional probabilities:

sometimes , we will see the Opposition that can be used to make the mess done. We will use the rule of independence such as :

# Editor's Note

“学吧,至少不亏.”一句良言 终身受用.

好友：

路漫漫其修远兮，吾将上下而求索。
--怪兽师傅

而很多时候，所谓的选择都是虚的，那是因为没有出现最好的那个选择。而没有出现最好的选择，是因为你还没有强大到吸引来那个最好的。
--Vamei学长

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#### 引用来自“紫电清霜”的评论

Machine Learning 4 - Naive Bayes朴素贝叶斯算法

2017-11-23@erixhao技术极客TechBooster AI 系列四，距上篇博文已经近一个半月之久了，是时候再动笔写一篇了，不然无法向几千个公众号读者粉丝交代，感谢大家不掉粉的同时还在增加。 本文将简...

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