2. Examples of random processes

2.1 Poisson process

The Poisson process is an event process with temporal or spatial support. In the temporal case, its support is continuous time, the random variable is 0 or 1 (the event occurs or not), it is memoryless (the occurrence at time t is independent of the occurrence at any other time), and it is characterized by its generally time-dependent intensity λ(t) expressed, for example, in number (of event occurrences) per second.

As a first step, let's assume λ to be constant and divide time into equal periods of duration...