Uniform distribution of random variable.

The continuous random variable X is evenly distributed in the interval [ a; c ] if its probability density in this interval is constant, i.e. if all values ​​in this interval are equally likely:

(8.1)

The value of the constant с is determined from the normalization condition:

. (8.2)

Distribution function:

, (8.3)

The numerical characteristics of a uniformly distributed random variable are defined as:

(8.4)

(8.5)

The standard deviation of the uniform distribution is

(8.6)

The uniform distribution of a random variable is completely determined by two parameters: a and b , the interval at which the random variable is defined.

If necessary, you can determine the parameters a and b of the uniform distribution of the known values ​​of the expectation m _X   and variance D _x random variable. For this, a system of equations is made up of the following form:

, (8.7)

from which the desired parameters are determined.

The probability of a uniformly distributed random variable falling into the interval [α, β) is determined as follows:

where

Continuous uniform distribution

Probability density
Distribution function
Designation	,
Options	, —Shift factor - scale factor
Carrier
Probability density	b \ end {matrix}">
Distribution function
Expected value
Median
Fashion	any number of segment
Dispersion
Asymmetry coefficient
Coefficient of kurtosis
Informational entropy
Generating function of moments
Characteristic function