Geometric Distribution: Definition, Properties and Application.

Statistical Aid - November 03, 2020

Geometric Distribution

A discrete random variable X is said to have a geometric distribution if its probability density function is defined as,

$f\left ( x;p \right )=pq^{x};x=0,1,2...,\infty$

where p is the only parameter of of geometric distribution which satisfy 0<=p<=1 and p+q=1.

Properties of Geometric Distribution

Geometric distribution follows the lack memory property.
The mean of geometric distribution is ${\frac {1-p}{p}}$ .
The variance of geometric distribution is ${\frac {1-p}{p^{2}}}$ .
Moment generating function of geometric distribution is ${\frac {p}{1-(1-p)e^{t}}}$ .
The mean of geometric distribution is smaller then its variance, since q/p2 > q/p.

Application of Geometric distribution

The Geometric distribution is used in Markov chain models.
It is used in meteorological modes of weather cycles and precipitation amounts.
The geometric distribution is often referred to as the failure time distribution.
It would be used to describe the number of interviews that have to be conducted by a selection board to appoint the first acceptable candidate.

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