Model the time between independent events occurring at a constant average rate.
Distribution Parameters
Average events per time unit (e.g., 2 calls/hour)
The point at which you want to calculate the probability.
Statistical Analysis
Cumulative Probability P(X ≤ x) (1.00)63.2121%
Mean (1/λ)1.0000
Std Deviation (σ)1.0000
PDF (Density)0.3679
Overview
The exponential distribution is the continuous analog of the Geometric distribution. It describes the time between independent events occurring at a constant average rate. It is widely used in physics, reliability engineering, and queuing theory.
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Pro Tips
The rate parameter λ must be positive (λ > 0).
The value x should be non-negative (x ≥ 0).
The mean of the distribution is 1/λ, which represents the average waiting time between events.
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Fun Facts
"The exponential distribution is memoryless: the probability of an event occurring in the next interval is independent of how much time has already passed."
"It is the only continuous distribution that has the memoryless property."
"Engineers use this to predict the Mean Time Between Failures (MTBF) for hardware components."
