The exponential distribution is a continuous probability distribution that is primarily concerned with the amount of time until a particular event occurs. It is commonly used in scenarios where events happen independently and at a constant average rate, such as the time between arrivals of buses or the time until a server fails. The distribution is defined by a single parameter, λ (lambda), which represents the rate of occurrence of events ²³.

One of the key properties of the exponential distribution is its memoryless nature, meaning that the probability of an event occurring in the future is independent of how much time has already elapsed. This characteristic makes it unique among continuous distributions ³. The probability density function (PDF) of the exponential distribution can be expressed mathematically, allowing for the calculation of probabilities related to waiting times ³.

In practical applications, the exponential distribution can be used to model various real-world scenarios, such as service times in queuing theory or the lifespan of electronic components ²³.