Mathematical statistics -- Sampling and sampling distribution

Quote ： The relationship between mathematical statistics and probability theory

• Both take the statistical law of random phenomena as the research object

• But there are great differences in the methods of studying problems ：

  • probability theory ： Known random variables obey a certain distribution , Seek the nature of distribution 、 Digital features and their applications ; It belongs to deductive method

  • mathematical statistics ： Through the statistical analysis of experimental data , Find the distribution and numerical characteristics that you obey , So as to infer the overall regularity , It belongs to induction

The core problem of mathematical statistics ： Infer the parent from the sub samples

Chapter one Sampling and sampling distribution

1.1 Mother and son

1.1.1 Mother

A statistical problem always has its specific research object .

Parent definition 1： The set composed of all the elements of the research object , Called the matrix or the whole .

Every element in the matrix is called an individual .

Parent definition 2： Some kind of research object （ Or something ） Quantitative indicators The whole of is called the whole , The quantitative index of each research object is called individual .

1.1.2 Maternal distribution

Maternal distribution ： Corresponding random variables X A probability distribution , Available distribution columns 、 Distribution density 、 The distribution function is specifically expressed .

Numerical characteristics of the parent distribution ： The numerical characteristics of the corresponding random variables .

notes：

• The matrix can be represented by random variables

• The maternal distribution is X The distribution of

• The numerical characteristics of the matrix are X The digital characteristics of

Parent definition 3： In mathematical statistics , Mother （ The overall ） Is a random variable that obeys a certain distribution , Call its probability distribution the overall distribution , Each individual corresponds to a random variable X A specific observation of .

1.1.3 Like

1.x Reference material

• Graduate student mathematical statistics Wang Rongxin Xi'an University of Electronic Science and Technology video