Random variable A random variable is a variable that takes an uncertain value. Since the event that takes place generating a particular value to the random variable is uncertain, some probability of occurrece can be attached to it. A random variable is discrete if it can only assume some numerical values. Example: the results in a test with 10 questions can be 0,1,2,...,10. A random variable is continuous when it can assume any value in an interval. Example: time between student arrivals at a professor's office during office hours (in minutes).