Poisson point process facts for kids
A Poisson process is a stochastic process. It counts the number of occurrences of an event leading up to a specified time. This is a counting process where the increments of time are independent of one another (the times do not overlap).
Definition
The counting process known as the Poisson process is defined as:
 N(0) = 0.
 N(t) has independent increments.
 The number of arrivals in any interval of length 𝜏 > 0 follows a Poisson distribution.
Where N(t) is the total number of events that occur by time t.
Images for kids

According to one statistical study, the positions of cellular or mobile phone base stations in the Australian city Sydney, pictured above, resemble a realization of a homogeneous Poisson point process, while in many other cities around the world they do not and other point processes are required.

An illustration of a marked point process, where the unmarked point process is defined on the positive real line, which often represents time. The random marks take on values in the state space S known as the mark space. Any such marked point process can be interpreted as an unmarked point process on the space [0,\infty]\times S . The marking theorem says that if the original unmarked point process is a Poisson point process and the marks are stochastically independent, then the marked point process is also a Poisson point process on [0,\infty]\times S . If the Poisson point process is homogeneous, then the gaps \tau_i in the diagram are drawn from an exponential distribution.
Mary Eliza Mahoney 
Susie King Taylor 
Ida Gray 
Eliza Ann Grier 