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An exponential random variable is a continuous probability distribution that describes the time between events in a Poisson point process. This process is characterized by events occurring continuously and independently at a constant average rate. The exponential distribution is a special case of the gamma distribution and is the continuous analogue of the geometric distribution1.
Probability Density Function (PDF)
The probability density function (PDF) of an exponential distribution is given by: [ f_X(x|\lambda) = \begin{cases} \lambda e^{-\lambda x} & \text{for } x > 0 \ 0 & \text{for } x \leq 0 \end{cases} ] where (\lambda) is the rate parameter2.
Mean and Variance
The mean ((E[X])) and variance ((Var(X))) of an exponential distribution are: [ E[X] = \frac{1}{\lambda} ] [ Var(X) = \frac{1}{\lambda^2} ]
Memoryless Property
I Last one has simple form for exponential random variables. We have PfY >ag= e a for a 2[0;1). I Note: X >a if and only if X 1 >a and X 2 >a. I X 1 and X 2 are independent, so PfX >ag= PfX 1 …
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Exponential Distribution (Definition, Formula, Mean & Variance ...
Learn about the exponential distribution, a continuous probability distribution that models the time between events in a Poisson process. Find out its formula, mean, variance, memoryless …
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What is the origin of exponential random variables? An exponential random variable is the inter-arrival time between two consecutive Poisson events. N + 1 Poisson counts. Question: Find …
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I Have various ways to describe random variable Y: via density function f Y (x), or cumulative distribution function F Y (a) = PfY ag, or function PfY >ag= 1 F Y (a). I Last one has simple …
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