Home | Command Reference | Run Example

Exponential_Dist Command

The Exponential_Dist command visualizes the Exponential distribution through probability and frequency-domain charts. The Exponential distribution is commonly used to model waiting times between randomly occurring events.

Main idea: analyze the probability of waiting for the next event in a random arrival process.

Example


Exponential_Dist(0.5)

This example creates an exponential distribution with arrival rate λ = 0.5.

Output Panels

Syntax


Exponential_Dist(lambda)

Mathematical Definition


f(x)=λe^(-λx)

for x ≥ 0.

The mean waiting time is:


1/λ

Interpretation

The Exponential distribution possesses the memoryless property. The probability of waiting an additional amount of time does not depend on how long one has already waited.

Applications

The Exponential distribution is closely related to the Poisson distribution. While the Poisson distribution models the number of events occurring in an interval, the Exponential distribution models the waiting time between those events.