The Exponential Distribution & Poisson Process 1

We finished discussing Discrete-Time Markov Chains in the previous lecture, and are now heading towards Continuous-Time Markov Chains. Discrete-time Markov Chains are totally synchronized, whereas CTMCs are not. In preparation for CTMCs, we need to discuss the Exponential distribution and the Poisson arrival process. We say that a random variable X is distributed exponentially with rate λ, X ∼ Exp(λ) if X has the probability density function: f (x) = λe −λx x ≥ 0 0 x < 0 The graph of the probability density function is shown in Figure 1. Notice that the exponential distribution drops off by a constant factor every timestep.