11.3: Specialized Probability Distributions
11.3.1 Exponential Distribution
The Exponential distribution is a probability distribution that is used to model the time between events in a Poisson point process. This process is characterized by the occurrence of events that happen continuously and independently at a constant rate, denoted by $λ$. In other words, the Exponential distribution is a continuous probability distribution that describes the amount of time it takes before an event occurs in a Poisson process.
This distribution is widely used in various fields, including engineering, economics, and physics, where it is used to model the time between occurrences of certain events. For example, the Exponential distribution can be used to model the time between failures of a mechanical system, the time between customer arrivals in a queue, or the time between radioactive decay events.
The Exponential distribution is a fundamental concept in probability theory and is an essential...