## What is the Exponential Distribution?

The exponential distribution, also known as the negative exponential distribution, is a probability distribution that describes time between events in a Poisson process. A Poisson process gives a way to find probabilities for random points in time for a process, and it is based on the Poisson distribution. There is a strong connection between the exponential distribution and the Poisson distribution. The Poisson distribution is a tool that helps to predict the probability of certain events occurring when you know how often the event has occurred. The exponential distribution models time between successive events over a continuous time interval, while Poisson distribution models events that happen over a fixed period of time.

### Why is this Useful?

The exponential distribution is most commonly used for testing product reliability. This distribution can be used to model waiting times, which can help answer questions about how long it will take for a certain outcome to result. The exponential distribution can also be used to model space between events, instead of time between events. This distribution has a memoryless property, which means that the length of time you wait for an event neither increases nor decreases the probability of an event happening. This property allows the exponential distribution to be very useful, but can limit the appropriateness for the distribution to be used in certain situations. Exponential distribution is also an important distribution for building continuous-time Markov chains.

### Applications of the Exponential Distribution

- Statistical Analysis
- Probability Theory