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Concept + formula (excluding parameter estimation)

2022-06-24 12:42:53Betula alnoides forest

Chapter one

1、 Not compatible with each other

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2、 Random event operation law

Commutative law 、 Associative law 、 Distributive law 、 The law of reflexion 、 Law of duality
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3、 Other properties of probability measures (6 strip +1 inference )

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4、 Conditional probability

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5、 All probability formula ( Compulsory examination )

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6、 Bayes' formula

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7、 The independence of the two events

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8、 Bernoulli experiment

There are only two events :

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n Heavy Bernoulli :

(1) Something happened k Time :

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(2) A certain event No k Time only :

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Chapter two

1、 Distribution function

It is applicable to both continuous and discrete types .
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2、 Probability density function

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3、 Mathematical expectation

discrete :
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Continuous type :
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nature :
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4、 variance

DX The original definition of :

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DX More commonly used formulas :

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5、 Discrete distribution and continuous distribution

Maybe I'll pass the exam : The binomial distribution 、 Poisson distribution 、 Uniform distribution 、 An index distribution 、 Normal distribution
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Book examples P79

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Example P80

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The third chapter

1、 Joint probability distribution ( form )

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2、 Joint distribution function

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3、 Probability density function

(1) Joint probability density :
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(2) Edge density function :
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4、 Conditional distribution

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5、X and Y Are independent of each other

necessary and sufficient condition :
(1)
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(2)
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Example ( Must master )

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6、 Conditional density function

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

8、 Linear combination of normal distribution

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9、 Two dimensional mathematical expectation

(1) Calculation of mathematical expectations :

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

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10、 covariance

(1) Original definition :( Know about )

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(2) Common formula :
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(3) nature :

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11、 The correlation coefficient

(1) The formula :
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(2) significance :

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(3) Irrelevant necessary conditions :

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12、 Central limit theorem

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13、 The definition of statistics

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Textbook examples

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14、 Chi square distribution 、F Distribution 、t Distribution

Chi square distribution :( Optional theorem )

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

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t Distribution :
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inference :
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The above is the speed sorting before the exam ( Not necessarily complete ).

END

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