Question

Exponential Distribution and Normal Distribution

06 Sep 2023
Answer :
Word Count : 376
Criteria Exponential Distribution Normal Distribution
Definition A probability distribution that describes the time between events in a Poisson process, where events occur continuously and independently at a constant average rate. A probability distribution that describes a continuous random variable with a symmetric, bell-shaped curve where most of the observations cluster around the central peak.
Probability Density Function (PDF) f(x;λ)=λe−λxf(x; \lambda) = \lambda e^{-\lambda x}f(x;λ)=λe−λx for x≥0x \geq 0x≥0, where λ\lambdaλ is the rate parameter. f(x;μ,σ)=12πσ2e−(x−μ)22σ2f(x; \mu, \sigma) = \frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}f(x;μ,σ)=2πσ2​1​e−2σ2(x−μ)2​, where μ\muμ is the mean ___ _______ ______ _______ ______ __________ ________ _______ ____ ___.
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