Understanding Random Variables Introduction to random variables and their significance in representing outcomes of experiments.
Motivating Example: Playing Monopoly Motivation behind defining a random variable using the example of playing Monopoly with dice rolls.
Defining Random Variables Functionally Definition of a random variable as a function mapping outcomes from sample space to real numbers.
Probability Derivation for Random Variables Deriving probabilities for specific values or sets from the original probability space through inverse functions.
Verifying Probability Axioms Verification that defined probabilities meet axioms including non-negativity, summing up to one, and countable additivity.
Properties of Pre-Images Illustrating properties like injectivity and disjointness in pre-images when dealing with multiple sets mapped by a function.