The exponential distribution with parameter λ > 0 has probability density function f(x) = λe^(-λx) for x ≥ 0, and cumulative distribution function F(x) = 1 - e^(-λx). The mean is E(X) = 1/λ and variance is Var(X) = 1/λ². It models the memoryless waiting time until the next event in a Poisson process.