Module 2:Poisson Process and Kolmorogov equations
  Lecture 6:Derivation of Poisson Process
 

Note
Let  denote the time from  until the first event occurs, then we have , i.e., .

Thus we have

We are already aware that , which denotes that in the time interval  the event occurs  number of times. Thus diagrammatically it is as follows which is illustrated in Figure 2.5.

Figure 2.5 : The notational concept of time ,  and the number of events within each time intervals (which is denoted using colour scheme for ease of understanding)