Definitions [3]
Definition: Continuous Random Variable
If the range of ( X ) is an interval (a, b), then ( X ) is called a continuous random variable.
Definition: Random Variable
Let ( S ) be the sample space associated with a given random experiment. Then, a real-valued function ( X ) which assigns an outcome \[w\in S\] to a unique real number X(w) is called a random variable.
Definition: Discrete Random Variable
If the range of the real function \[X:U\to R\]is a finite set or an infinite set of real numbers, then X is called a discrete random variable.
