概率论高速学习03:概率公理补充

Posted

tags:

篇首语:本文由小常识网(cha138.com)小编为大家整理,主要介绍了概率论高速学习03:概率公理补充相关的知识,希望对你有一定的参考价值。


原创地址:   http://www.cnblogs.com/Alandre/  (泥沙砖瓦浆木匠),须要转载的,保留下! Thanks

  “应注意到一个析取命题的对立命题是由该析取命题各部分的对立内容构成的一个合取命题” ——奥卡姆的威廉著。《逻辑学论文》


Written In The Font

  I  like maths when i was young,but I need to record them. So I am writing with some demos of Python

 

Content

  If two events, A and B are independent then the joint probability is

   技术分享

          技术分享                                         

 

For example, if two coins are flipped the chance of both being heads is

技术分享

 

In Python

A = set([1,2,3,4,5])
B = set([2,4,3,5,6])
C = set([4,6,7,4,2,1])

print(A & B & C)

Output:

{2, 4}

# & find the objects  the same in Set


         

   If either event A or event B or both events occur on a single performance of an experiment this is called the union of the events A and B denoted as:

   技术分享.

  If two events are mutually exclusive then the probability of either occurring is

  技术分享

            技术分享

 

For example, the chance of rolling a 1 or 2 on a six-sided die is

 技术分享

 

In Python

A = set([1,2,3,4,5])
B = set([2,4,3,5,6])
C = set([4,6,7,4,2,1])

print(A | B | C)

Output:

{1, 2, 3, 4, 5, 6, 7}

# | find all the objects the set has


  If the events are not mutually exclusive then

  技术分享

Proved

  技术分享

 

For example:

  Let’s use Python to show u an example about devil‘s bones (骰子,不是 魔鬼的骨头哈技术分享)

技术分享
A = set([1,2,3,4,5,6])  # the all results of devil‘s bones
B = set([2,4,3])        # the A event results 
C = set([4,6])          # the B event results 

P_B =  1/2
P_C =  1/3

D = B | C
print(D)

P_D = 2/3

print(P_D == (P_B+P_C - 1/6))
技术分享

Output:

{2, 3, 4, 6}
True

 


Let me show u some others :


         技术分享 
         技术分享 
         技术分享 
         技术分享 
        技术分享 

 

If u r tired , please have a tea , or look far to make u feel better.If u r ok, Go on!


  Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written:

   技术分享,

   Some authors, such as De Finetti, prefer to introduce conditional probability as an axiom of probability:

技术分享

Given two events A and B from the sigma-field of a probability space with P(B) > 0, the conditional probability of A given Bis defined as the quotient of the probability of the joint of events A and B, and the probability of B:  

  技术分享

  the ①② expressions  are the same. Maybe u can remember one , the other will be easy to be coverted.So I am going to tell an excemple to let u remmeber it(them):

  

  “the phone has a power supply (B), the phone can be used to call others(A).”

  One →  技术分享 : When the phone has a full power supply , u can call others.

  Two →P(B): has   a power supply           

  Three = One +  Two → U can call others about your love with others.

 

do u remember it?

                                                                 技术分享

 

Editor‘s Note

    “路漫漫其修远兮,吾将上下而求索”

 

The Next

            cya soon. We meet a big mess called The total probability and Bayes .

 

      The total probability

      技术分享
      技术分享

      Bayes (Thomas, 1702-1761,) ; 

       技术分享

if u wanna talk with me , add the follow:

 

技术分享









以上是关于概率论高速学习03:概率公理补充的主要内容,如果未能解决你的问题,请参考以下文章

人工智能数学基础--概率与统计9:概率运算加法公理事件的独立性概率乘法定理条件概率全概率公式以及贝叶斯公式

现代概率论03:测度空间

概率论小课堂:公理化过程(大数据方法解决问题的理论基础)

概率论公理

概率论02 概率公理-集合

概率:概率的公理化定义