\[f(x)=\lambda e^{-\lambda x}\]
Variables
fprobability density
xrandom variable value
lambdarate parameter
Description
What is this formula?
This formula calculates the probability density of an exponential distribution. It models the time between independent random events occurring at a constant average rate.
When to use it
Use this formula when analyzing waiting times, lifetimes, or intervals between events in random processes.
Example
If failures occur on average 3 times per hour, the formula can estimate the probability density associated with a waiting time of 20 minutes.
Applications
Reliability engineering, queueing systems, telecommunications, radioactive decay analysis, maintenance planning, and stochastic processes.