### Exponential Distribution

A continuous random variable X is said to have an exponential distribution with parameter Î¸ if its probability density fumction is defined as,

where, Î¸ is the only parameter of the distribution and Î¸>0. Exponential distribution is continuous probability distribution and it has memoryless property like geometric distribution.

### Characteristics of Exponential Distribution

- Exponential distribution has only one parameter ‘Î»’.
- Mean of exponential distribution (variate) is 1/Î».
- Variance of exponential distribution (variate) is 1/Î»
^{2}. - Moments of all order exists in exponential distribution.
- Characteristic function of exponential distribution is .
- Moment generating function of exponential distribution is .
- Median of exponential distribution is also 1/Î».
- The
measure of skewness Î²
_{1}= 4. - Measure of kurtosis, Î²
_{2}= 6. These measures show that exponential distribution is positive skewed and leptokurtic. - If the value of Î»=1; mean= variance, if Î»<1; mean<variance and if Î»>1; mean>variance.
- It also process the memoryless property just like geometric distribution.

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