Distribution of a Function of a Random Variable

Some special distributions

There are several parametric families of univariate radom varaible.

Sketches of most are given, the mean and variance of each are derived, and usually examples of random

experiments which the defined parametric family might provide arealistic model are included

There are the following distributions . Uniform,Poisson, Bernolli, Binomial,Negative Binomial, Geomertric, and

Hypergometic as special distributions of fiscret random variables

And Exponential, Normal, Beta,Gamma, Chi-Square,.....

A discrete probability distribution shall be understood as aprobability distribution characterized by a

probability mass function.

Thus, the distribution of arandom variable X is discrete, radom variable

,if sum of Pr(X=u) over the values of X=1

This random variable takes its values from the finite or countably infinite number set of values .

Mathematicaly, we can call such distributions absolutely continuous,since its cumulative distributionfunctionis absolutely continuous with respect to the Lebesgue measure

function is absolutely continuous with respect to the Lebesgue measure ?. If the distribution of X is continuous, then X is called a continuous random variable. There are many examples of continuous probability distributions: normal, uniform, chi-squared, and others.