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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.
Exponential_Dist(0.5)
This example creates an exponential distribution with arrival rate λ = 0.5.
Exponential_Dist(lambda)
lambda – average event arrival rate
f(x)=λe^(-λx)
for x ≥ 0.
The mean waiting time is:
1/λ
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.
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.