Random Variables on a Countable Space

Abstract

In Chapter 5 we again assume Ω is countable and A=2^Ω. Random variable X in this case is defined to be a function from Ω into a set T. A random variable represents an unknown quantity (hence the term variable) that varies not as a variable in an algebraic relation (such as x²−9=0), but rather varies with the outcome of a random event. Before the random event, we know which values X could possibly assume, but we do not know which one it will take until the random event happens. This is analogous to algebra when we know that x can take on a priori any real value, but we do not know which one (or ones) it will take on until we solve the equationx²-9=0 (for example).