Ever wondered how to calculate the time between events in a Poisson process? The answer lies in the exponential distribution, a key concept in probability theory.
Get to Know the Probability Density Function
Introducing the Cumulative Distribution Function
\[\large F(x ; \lambda ) = \left\{\begin{matrix} 1 – e^{-\lambda x} & x>= 0,\\ 0 & x < 0. \end{matrix}\right.\]
Note that
Now, let's delve into the mean of the
Exponential (
) Distribution
. This is where integration by parts comes into play –
Let's simplify this further,