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Discrete random variables

Lecture



x i - values ​​of X ,

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Expected value

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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

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Initial moment of order k of random variable X

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Central moment of order k of random variable X

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Binomial distribution law

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Poisson law

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The law of large numbers

Chebyshev Inequality

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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.


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Probability theory. Mathematical Statistics and Stochastic Analysis

Terms: Probability theory. Mathematical Statistics and Stochastic Analysis