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Exponential probability density function formula |
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Answer» The PROBABILITY density function (pdf) of an exponential distribution is {\displaystyle f(x;\lambda )={\begin{cases}\lambda e^{-\lambda x}&x\geq 0,\\0&x<0.\end{cases}}}Alternatively, this can be defined using the right-continuous HEAVISIDE step function, H(x) where H(0)=1: {\displaystyle f(x;\lambda )=\mathrm {\lambda } e^{-\lambda x}H(x)}Here λ > 0 is the parameter of the distribution, often called the rate parameter. The distribution is supported on the interval [0, ∞). If a random variable X has this distribution, we write X ~ Exp(λ). The exponential distribution exhibits infinite divisibility. |
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