Combining random variables
Random variables are neither "random" nor "variable". However, by defining arithmetic operations on them, we can put them into equations, where they can act like variables.
Note: You cannot add random variables on different sample spaces.
Similarly, we can define other operations:
For example, suppose we modeled an experiment where we randomly selected a rectangle from a given set. We might have random variables and that give the width and height of the selected rectangle. We could then define a new "area" random variable by multiplying and ; this would work as expected: to find the area of a given outcome, you would measure the width and the height and then multiply them (since by definition, ).