ABSTRACT
In the first course of probability, we learned that a random variable is a variable that takes on a set of possible different values by chance. While this intuitive definition is sufficient for simple computations with stand-alone random variables, the analysis of stochastic processes, which are collections of random variables, requires a different way of thinking, which is to treat random variables as functions. Then we could use calculus of functions to compute interesting random variables arising from applications of stochastic processes.
