Probability theory high-speed learning 03: probability axiom Supplement

Original address: http://www.cnblogs.com/Alandre/(mud brick slurry carpenter), need to reprint, keep under! Thanks

"It should be noted that the opposite proposition of a disjunctive proposition is a combined proposition composed of the opposing contents of each part of the proposition"-William of Occam. The thesis of logic

Written in the Font

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

Content

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

 

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

In Python

A = set ([1,2,3,4,5= set ([2,4,3,5,6= 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 Calle D The union of the events A and B denoted as:

.

If The events are mutually Exclusive Then the probability of either occurring is

　　

　　　　　　　　　　　　

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

In Python

A = set ([1,2,3,4,5= set ([2,4,3,5,6= set ([4,6,7,4,2,1])print(A | D: C

Output:

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

# | Find all the objects the set have

If The events is not mutually exclusive then

　　

Proved

　　

For example:

Let 's use Python-show u An example about Devil's bones (dice, not Devil's Bones ha )

A = Set ([1,2,3,4,5,6])#The all results of devil ' s BonesB = Set ([2,4,3])#The A Event resultsC = Set ([4,6])#The B Event resultsp_b= 1/2P_c= 1/3D= B |CPrint(D) p_d= 2/3Print(P_d = = (P_B+P_C-1/6))

Output:

{2, 3, 4, 6} True

Let me show u some others:

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 and other event B. Conditional PR Obability is written:

,

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

①

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

Ii

The①②expressions is the same. Maybe u can remember one, the other'll be an easy-to-be coverted. So I am going to tell a excemple to let U remmeber it (them):

　　

"The phone has a power supply (B) and the phone can be used to call others (a)."

one→: When the phone have a full power supply, u can call others.

Two→p (B): Has a power supply

three = one + Two→u can call others on your love with others.

Do u remember it?

Editor ' s Note

"The road long its repair far XI, I will go up and down and quest"

The Next

CYA soon. We meet a big mess called the total probability and Bayes .

The total probability

　　　　　　
　　　　　　

Bayes (Thomas, 1702-1761,);

if u wanna talk with me, add the follow:

Probability theory high-speed learning 03: probability axiom Supplement