The most fundamental concept in probability theory is the random variable. We will not be able to analyze the formal definition of a random variable as this is very technical. However, we will be able to develop an understanding of a random variable and this is all we need. It will turn out to be useful to distinguish between discrete random variables and continuous random variables. Random variables are intimately connected to their distribution functions and this will be discussed in detail. Finally, we look at a specific random variable, the standard normal random variable. The standard normal has the well known bell-shaped density function.