Discrete Uniform Distribution

Introduction

Much of this class is about notation. The next section attempts to build on your experience about dice in an effort to minimize the mental hurdles that follow this new notation. Expanding on the process of rolling a single die, we introduce a more formal definition of a random variable. Despite it’s name, random variables are 1) not random and 2) not variables. They get this name nonetheless because we think of them as variables that take on random values.

Using a fair die as an example of a random variable, we introduce a particular, but not the only, notion of probability. While it’s easy to get lost in the new notation and naturalness of this interpretation of probability, don’t lose sight of the world’s most interesting processes. Random variables are not always repeatable in an operational manner, and thus it’s not always obvious how probability is meant to be understood in tese contexts.