Topic 1: Random Variables

This set of handwritten study notes provides a structured foundation in Probability and Random Variables, perfect for students tackling introductory statistics or discrete mathematics. It breaks down complex concepts into clear, handwritten definitions and visual examples, moving from basic probability rules to advanced theorems. These notes have helped me a lot in understanding this topic. What’s Included: 1. Probability Foundations: Detailed explanations of sample spaces, events (complementary, intersection, union), and disjoint events. 2. Core Axioms & Rules: A breakdown of the three fundamental probability axioms, the complement rule, and the addition rule for non-disjoint events. 3. Conditional Probability & Independence: Formulas and worked examples for P(A|B), independent vs. dependent events, and the Multiplication Rule. 4. Advanced Theorems: Step-by-step guides for the Law of Total Probability and Bayes' Theorem, including a full medical testing word problem. 5.Random Variables: Comprehensive coverage of both Discrete (PMF, countable values) and Continuous (PDF, integration, CDF) random variables. Why These Notes? 1. Exam-Ready Examples: Includes practical scenarios like coin tosses, die rolls, and medical diagnostic probability calculations. 2. Visual & Logical Flow: Organized with clear headings and boxed formulas for quick reference during study sessions. 3. Calculus Integration: Clearly explains how to use integration to find the area under a Probability Density Function (PDF).Whether you are preparing for a mid-semester test or need a solid refresher on the Law of Total Probability, these notes offer a concise and high-quality summary of the essential curriculum.