IB Maths AA SL 4.7 - Discrete Random Variables and Expected Value

This IB Maths AA SL Topic 4.7 – Discrete Random Variables and Expected Value resource develops students’ understanding of discrete probability distributions and their applications. It begins by defining a discrete random variable as a variable that can take only a finite number of possible values. Students learn how to represent discrete probability distributions using tables and functions, check that all probabilities are valid, and confirm that the probabilities sum to 1.

The lesson also introduces discrete uniform distributions, where each possible outcome has probability 1/n, and develops students’ ability to determine unknown constants within probability models. Students then learn how to calculate expected value using E(X) = the sum of xP(X = x) and interpret it as the long-term average or mean of a distribution. The resource applies expected value to games of chance, including calculating expected winnings, accounting for participation costs, and determining whether a game is fair. With clear definitions, probability tables, worked examples, challenging practice questions, financial applications, and fully worked solutions, this resource helps SL students build strong probability and decision-making skills in line with IB Mathematics AA expectations.