distinguish between the exponential distribution and the poisson distribution

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Expert Solution

Below are the differences between the exponential distribution and the poisson distribution

Exponential Distribution	Poisson Distribution
It is a continuous distribution with the random variables taking positive real values.	It is a discrete distribution with the random variables taking positive integer values 0, 1, 2,..
It deals with the time between occurrences of successive events	It deals with the number of occurrences in a fixed period of time or region.
The probability distribution with rate parameter is, P(X = x) = exp(-x)	The probability mass function with rate parameter is, P(X = x) = exp(-) / x!
Exponential distribution is a memoryless distribution. That is, P(X > a + b \| X > a) = P(X > b) holds for exponential distribution	Poisson distribution is not a memoryless distribution.
The time interval, between two Poisson events follows exponential distribution.	The number of occurrence of events in a fixed time interval follows Poisson distribution.

orchestra answered 11 months ago

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