Randomized Algorithms (Spring 2010)/Balls and bins

Random Variables and Expectations

What do we mean by the sentence "[math]\displaystyle{ X }[/math] is a random variable"? I guess most os us just imagine that [math]\displaystyle{ X }[/math] is like a random dice whose value is ranging over a set [math]\displaystyle{ R }[/math] of values, and [math]\displaystyle{ X }[/math] is randomly equal to some element of [math]\displaystyle{ R }[/math], like we saying that "[math]\displaystyle{ X }[/math] is distributed over [math]\displaystyle{ R }[/math]".

While this intuition is quite convenient for us and works most of times, we need a more formal definition of random variables