A random variable is a function that associates a real number to each element of the sample space, S.
Capital letters are used X, Y, ... to denote random variables and the lower case letters (x, y, ...) to denote the respective specific values.
Discrete Random Variable
A discrete random variable is one that can only take an integer value.
The number of children in a family, the score obtained by throwing a dice.
Continuous Random Variable
A continuous random variable is one that can take all possible values within a certain interval.
The height of students in a class, the hours of duration of a battery.