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
random,
if it can receive real values with definite probabilities
as a
result of experiment. The random variable X is called discrete,
if such nonnegative function exists
which determines the correspondence
between a value õ_{i}
of the variable
Õ
and
the probability
ð_{i} , that
X
receives this value.
Discrete random variables
X
and
Y
are called
independent
random variables, if the events
Õ
= õ_{i
}and
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
nonnegative 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
distribution function
of random variable X
and marked as F (
x
) :
F
(
x
) =
Ð
(
X
x
) .
General properties of distribution function:
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