

This IB Math AI SL 4.7 – Discrete Random Variables & Expected Value resource builds students’ understanding of how numerical outcomes from random processes are modelled and analysed. Students learn to distinguish discrete from continuous variables, work with probability mass functions (pmfs), verify valid distributions, and calculate expected value as the long-run average outcome. Applications to games of chance and fair pricing help connect theory to decision-making contexts.
Structured tasks progress from vocabulary and classification to using functions to define pmfs, finding unknown constants, computing expected value from tables, and analysing expected gains in real-life game and insurance scenarios. Extended problems develop deeper reasoning with algebraic expected value expressions, fairness conditions, and multi-step probability models. With scaffolded practice, exam-style questions, and a full answer key, this resource supports SL classroom teaching and independent study in line with IB Mathematics AI expectations.
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