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Discrete random variables

Lecture



x i - values ​​of X ,

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables


Expected value

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables

Properties:

1) M ( C ) = C , C is a constant;

2) M ( CX ) = CM ( X );

3) M ( X 1 + X 2 ) = M ( X 1 ) + M ( X 2 ), where X 1 , X 2 are independent random variables;

4) M ( X 1 X 2 ) = M ( X 1 ) M ( X 2 ).


Dispersion

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables

Properties:

1) D ( C ) = 0;

2) D ( CX ) = C 2 D ( X );

3) D ( X 1 + X 2 ) = D ( X 1 ) + D ( X 2 ), where X 1 , X 2 are independent random variables.


Standard deviation of random variable X

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables

Initial moment of order k of random variable X

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables


Central moment of order k of random variable X

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Binomial distribution law

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables

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Poisson law

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables


The law of large numbers

Chebyshev Inequality

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables

Chebyshev theorem

  Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables   Discrete random variables

X i - pairwise independent random variables;   Discrete random variables   Discrete random variables ; C is a constant.

See also


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Probability theory. Mathematical Statistics and Stochastic Analysis

Terms: Probability theory. Mathematical Statistics and Stochastic Analysis