**
Random variables
**

**
**

*
Random variable. Discrete and
continuous random variables.
*

*
Independent random variables.
Density function.
*

*
Distribution function.
*
*
General properties of distribution function.
*

A variable is called
**
**

**, if it can receive real values with definite probabilities as a result of experiment. The random variable**

*random**X*is called

**, if such non-negative function exists**

*discrete*

which determines the correspondence
between a value
*
õ
_{
i
}
*
of the variable

*Õ*and the probability

*ð*, that

_{ i }*X*receives this value.

Discrete random variables
*
X
*
and
*
Y
*
are called
**
independent
**

**, if the events**

*random variables*

*Õ*=

*õ*and

_{ i }

*Y*=

*y*

_{ j }**are independent**

**for arbitrary**

*i*and

*j*.

The random
variable
*
X
*
is
called a
**
continuous random
variable
**
,
if for
any
numbers

*a < b*such non-negative function

*f*(

*x*) exists, that

The function
*
f
*
(
*
x
*
)
is called a
**
density function
**
of continuous random variable
.
The probability of the
fact that a random variable

*X*receives a value less than

*x*, is called a

**of random variable**

*distribution function*

*X*and marked as

*F*(

*x*) :

*
F
*
(
*
x
*
) =
*
Ð
*
(
*
*
*
X
*
*
x
*
) .

**
General properties of distribution function:
**