Question

exponential probability density function formula

Answer 1

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.