Quick learning of probability theory 03: probability theory supplement

Original address: http://www.cnblogs.com/Alandre/ (sand tile pulp carpenter), need to reprint, keep the next! Thanks

"We should note that the opposite proposition of a proposition is a Union proposition composed of the opposite content of each part of the proposition." -- William of OCCAM, logical paper

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,AAndBAre independent then the joint probability is

　　

　　　　　　　　　　

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

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 eventAOr eventBOr both events occur on a single performance of an experiment this is called the union of the eventsAAndBDenoted:

.

If two 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])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

　　

Proved

　　

For example:

Let's use Python to show u an example about dedevil's bones (Dice, not the devil's bone)

A = set([1,2,3,4,5,6])  # the all results of devil's bonesB = set([2,4,3])        # the A event results C = set([4,6])          # the B event results P_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 other event B. Conditional probability is written:

,

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

①

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:

②

The ① ② 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 ()."

One →: 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?

Editor's Note

"The road is long, and I will try again and again"

The Next

Cya soon. We meet a big mess calledThe total probabilityAndBayes.

The total probability

　　　　　　
　　　　　　

Bayes (Thomas, 1702-1761 ,);

　　　　　　

If u wanna talk with me, add the follow: