S1 Definition

The Poisson Distribution is different from discrete finite distributions in that it has a range of possible outcomes over all integers, going from 0,1,2,... without any upper limit. This makes it a mathematical idealization, a model, since all real world processes are bounded above by some finite quantity. However, for mathematical purposes, it is useful to ignore the imperfections of the real world, and create a perfect and idealized model. The key to the Poisson is the standard definition of the exponential function:

Khan Academy: Lessons on Summation Notation - This notation is very important, and students are extremely ignorant about its meaning and correct usage. All STRONGLY encouraged to go through this brief lesson CAREFULLY.