Random Variable and Bivariate Probability Distribution **Definition of a Random Variable:** A random variable is a function that assigns numerical values to the outcomes of a random experiment. It can be discrete (taking countable values) or continuous (taking any value in an interval).

A random variable is a real-valued function that assigns a numerical value to each outcome in the sample space of a random experiment. A random variable is discrete if it takes finitely many or countably many values, each with a probability $P(X=x)$ (the probability mass function) satisfying