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Continuous random variables

Lecture



Integral function (distribution function)

Continuous random variables Continuous random variables Continuous random variables Continuous random variables

Properties:

one) Continuous random variables Continuous random variables Continuous random variables ;

2) Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables ;

3) Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables ;

four) Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables .


Differential distribution function (probability density)

Continuous random variables Continuous random variables Continuous random variables Continuous random variables

where F ( x ) is an integral function.

Properties:

one) Continuous random variables Continuous random variables ;

2) Continuous random variables Continuous random variables Continuous random variables ;

3) Continuous random variables Continuous random variables Continuous random variables ;

four) Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables .


Numerical characteristics of a continuous random variable

Expected value

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables


Dispersion

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables

Some laws of the distribution of continuous random variables

Uniform distribution

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables


Normal distribution (Gaussian distribution)

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables

Where Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables - Laplace function;

Continuous random variables Continuous random variables Continuous random variables Continuous random variables Continuous random variables

See also

created: 2014-10-25
updated: 2024-11-14
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Probability theory. Mathematical Statistics and Stochastic Analysis

Terms: Probability theory. Mathematical Statistics and Stochastic Analysis