Poisson Process Time Interval Calculator

Mathematical Foundation:

Time intervals between consecutive events follow exponential distribution with rate λ.

Key Properties:

• • Mean: $E[T_n] = \frac{1}{\lambda}$
• • Variance: $D[T_n] = \frac{1}{\lambda^2}$
• • Distribution: Exponential distribution Exp(λ)
• • Memoryless Property: $P\{T_n > t+s \mid T_n > s\} = P\{T_n > t\}$
• • Independence: T₁, T₂, ... are independent and identically distributed