Chapter one

1、 Not compatible with each other

2、 Random event operation law

Commutative law 、 Associative law 、 Distributive law 、 The law of reflexion 、 Law of duality

3、 Other properties of probability measures （6 strip +1 inference ）

4、 Conditional probability

5、 All probability formula （ Compulsory examination ）

6、 Bayes' formula

7、 The independence of the two events

8、 Bernoulli experiment

There are only two events ：

n Heavy Bernoulli ：

（1） Something happened k Time ：

（2） A certain event No k Time only ：

Chapter two

1、 Distribution function

It is applicable to both continuous and discrete types .

2、 Probability density function

3、 Mathematical expectation

discrete ：

Continuous type ：

nature ：

4、 variance

DX The original definition of ：

DX More commonly used formulas ：

5、 Discrete distribution and continuous distribution

Maybe I'll pass the exam ： The binomial distribution 、 Poisson distribution 、 Uniform distribution 、 An index distribution 、 Normal distribution

Book examples P79

Example P80

The third chapter

1、 Joint probability distribution （ form ）

2、 Joint distribution function

3、 Probability density function

（1） Joint probability density ：


（2） Edge density function ：

4、 Conditional distribution

5、X and Y Are independent of each other

necessary and sufficient condition ：
(1)

(2)

Example （ Must master ）

6、 Conditional density function

Textbook examples

Pay attention to uniform distribution ：f（x）= 1 / area
Integral time ：y The scope is [0,√1-x² ]
Finally, the scope of the summary is ： Conditional distribution Molecular range

7、 Convolution formula （ It's very important , But not this time ）

8、 Linear combination of normal distribution

9、 Two dimensional mathematical expectation

（1） Calculation of mathematical expectations ：

（2） nature ： Pay special attention to the situation of mutual independence ！

10、 covariance

（1） Original definition ：（ Know about ）

（2） Common formula ：

（3） nature ：

11、 The correlation coefficient

（1） The formula ：

（2） significance ：

（3） Irrelevant necessary conditions ：

12、 Central limit theorem

13、 The definition of statistics

Textbook examples

14、 Chi square distribution 、F Distribution 、t Distribution

Chi square distribution ：（ Optional theorem ）

F Distribution ：（ Be sure to see clearly n and m）

t Distribution ：

inference ：

The above is the speed sorting before the exam （ Not necessarily complete ）.

END