Question

State and prove lack of memory property of exponential distribution and interpret it.

Answer 1

The exponential distribution is one of the widely used continuous distributions. It is often used to model the time elapsed between events. We will now mathematically define the exponential distribution, and derive its mean and expected value. Then we will develop the intuition for the distribution and discuss several interesting properties that it has.

A continuous random variable X is said to have an exponential distribution with parameter λ>0, shown as X∼Exponential(λ), if its PDF is given by

fX(x)={λe−λx0x>0otherwise