Exponential Probability Distribution Calculator
Exponential Probability Distribution Calculator helps determine probabilities for events following exponential distribution, commonly used in reliability engineering and queueing theory. It calculates either the Probability Density Function (PDF) or Cumulative Distribution Function (CDF) for given rate parameter (λ) and time value (x).
Calculator
Formula
PDF: f(x; λ) = λe-λx
CDF: F(x; λ) = 1 - e-λx
How to Use
Enter the rate parameter (λ > 0) and x value (≥ 0). Click either PDF to get the probability density at x, or CDF to get the probability of X ≤ x. The clear button resets all fields. Results appear instantly with calculation details.
Derivation Process
The exponential distribution models time between events in Poisson processes. Derived from Poisson's axioms, it assumes events occur continuously/independently at constant rate λ. The PDF represents event likelihood at exact time x, while CDF accumulates probabilities from 0 to x, derived using integration of PDF.