# Geometric Distribution: Definition, Properties and Applications

### Geometric Distribution

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

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

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 .
• The variance of geometric distribution is .
• Moment generating function of geometric distribution is .
• 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.