X
has
binomial distribution
, if its possible values 0, 1, 2...,
m
, …,
n
, and probabilities corresponding them are equal to:
(21)
where 0 <
As shown from (21), probabilities
Example is selective quality assurance of industrial products at which selection of products for test is made on the scheme of casual
Binomial distribution is defined by the two parameters:
(22)
X
has
Poisson’s distribution
if it has infinite calculating set of possible values 0, 1, 2...,
m
, …, and probabilities corresponding them are defined by the formula:
(23) Examples of the casual phenomena, subordinated to Poisson’s distribution law, are: sequence of radioactive disintegration of particles, sequence of refusals at work of complex computer system, a stream of applications on a telephone exchange and many other things.
Poisson’s distribution law (23) depends on one parameter
(24)
X
has geometrical distribution, if its possible values 0, 1, 2...,
m
, …, and probabilities of these values:
(25)
where 0 <
Probabilities
m
form a geometrical progression with the first member
р
and denominator
q
, whence and the name «geometrical distribution».
As an example we’ll consider shooting on some purpose
Geometrical distribution is defined by one parameter
(26)
X
has hyper geometrical distribution with parameters
a
,
b
,
n
, if its possible values 0, 1, 2, ... ,
m
, … ,
a
have probabilities:
(27)
Hyper geometrical distribution arises, for example, when from an urn containing
(28) |

Contents
>> Applied Mathematics
>> Mathematical Statistics
>> Elements of Mathematical Statistics
>> Distributions of discrete random variables