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Exponential distribution is a continuous probability distribution that models the time between events in a Poisson process.

The exponential distribution is often used to model the time between events in a Poisson process, where events occur randomly and independently at a constant rate. For example, the time between arrivals of customers at a store or the time between radioactive decay events can be modelled using the exponential distribution.

The probability density function (PDF) of the exponential distribution is given by:

f(x) = λe^(-λx)

where λ is the rate parameter, which represents the average number of events per unit time, and x is the time between events.

The cumulative distribution function (CDF) of the exponential distribution is given by:

F(x) = 1 - e^(-λx)

which gives the probability that the time between events is less than or equal to x.

The mean and variance of the exponential distribution are given by:

E(X) = 1/λ

Var(X) = 1/λ^2

The exponential distribution has the memoryless property, which means that the probability of an event occurring in the next time interval does not depend on how much time has already elapsed. This property makes the exponential distribution useful in reliability analysis and queueing theory.

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