lets say that X is some random variable that takes +1 if rational otherwise -1. at http://tutorial.math.lamar.edu/Classes/CalcI/TheLimit.aspx in example 4, can we consider g(x) as a random variable because it's behaviour is same, right? is random variable really random or just function? I found this very interesting notes on random variable: http://web.simmons.edu/~benoit/Markov%20+%20Stochastic%20Readings%20%28Net%29/s05_03n.pdf [Broken] it says that a random variable - is a function, not a variable - is a specific mapping, and not random So a random variable is neither random nor variable. Actually, I want to ask that if it is not random and not variable then why is it called random variable? I guess that we call it random variable because we don't want to mix it up with variable that we use in ordinary calculus/engineering-calc, am I right? Thanks in advance.