Random processes exist everywhere. Roughly speaking, a random process is a system of related random variables, usually indexed with respect to time t ≥ 0, for a continuous random process, or by natural numbers n = 1, 2, …, for a discrete random process. Many (discrete) random processes satisfy the Markov property, which makes them a Markov chain. The Markov property is the statement that the process is memoryless, in that only the current value is important for the probabilities of the next value.
In this recipe, we will examine a simple example of a random process that models the number of bus arrivals at a stop over time. This process is called a Poisson process. A Poisson process N(t) has a single parameter, λ, which is usually called the intensity or rate, and the probability that N(t) takes the value n at a given time t is given by the following formula:
This equation describes...
