Exponential Distribution Probability
Exponential Distribution Probability
\[f(x)=\lambda e^{-\lambda x}\]
Variables
f = probability density
x = random variable value
lambda = rate 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.
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