### Definition

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

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.