Exponential Distribution Calculator
Calculate probabilities for the exponential distribution, which models the time between independent events occurring at a constant rate. Find CDF, survival function, and PDF values.
The exponential distribution models waiting times between events in a Poisson process.
PDF: f(x) = λe^(-λx) for x ≥ 0 CDF: F(x) = 1 - e^(-λx) Survival: S(x) = e^(-λx) = P(X > x)
Key Properties:
- Mean = 1/λ
- Variance = 1/λ²
- Median = ln(2)/λ
- Memoryless property: P(X > s+t | X > s) = P(X > t)
Applications: Time between customer arrivals, equipment failure times, radioactive decay.