Statistics 2

Abstract

This pedagogical handout provides a complete course in probability theory for first-year LMD students of the Basic Education Department in Economic, Commercial and Management Sciences Faculty at SETIF 1 University Ferhat Abbas. The material is organised into three progressively structured chapters. Chapter 1 presents the mathematical foundations of probability: sample spaces and events, the three definitions of probability (classical, empirical, axiomatic), the addition and multiplication rules, conditional probability, total probability, Bayes' theorem, and combinatorial analysis. Chapter 2 develops the theory of random variables, both discrete (PMF, CDF) and continuous (PDF, CDF), together with their numerical summaries, including expected value, variance, standard deviation, and the Z-score used for standardization. Chapter 3 completes the course with the seven most important named probability distributions used in economics and management: Bernoulli, Binomial, Hypergeometric, and Poisson (Discrete Random Variables); Uniform, Exponential, and Normal (Continuous Random Variables). Each family is introduced through its generating mechanism, its PMF or PDF, its moments, and representative economic applications. Approximations between distributions (Binomial →Poisson, Binomial→ Normal, Poisson →Normal) are discussed with their validity conditions. Three reference tables (standard normal, selected binomial, selected Poisson) are provided as appendices to Chapter 3. The handout features 11 full-page mind maps that visually summarise the key concepts, more than 55 worked examples set in economic and managerial contexts, and 58 unsolved practice exercises graded on three levels (foundations, applications, extension). Each chapter includes learning objectives, common-mistake warnings, and revision-oriented summary cards.