Probability Theory and Simulation with Python

Understanding probability goes far beyond memorizing formulas and plugging in numbers. Real insight comes from observing random processes and modeling them directly. This written course guides you through foundational probability theory by combining core mathematical principles with practical Python simulations. You will start with key definitions, sample spaces, and classical probability before advancing to discrete and continuous random variables. As you progress, you will read through step-by-step written explanations and code examples that model random events, bring distributions to life, and demonstrate limit theorems empirically. What you will learn: Understand essential probability terminology, sample spaces, and foundational axioms. Explore discrete and continuous probability distributions with clarity. Calculate expected value, variance, and conditional probability accurately. Simulate probabilistic experiments and random variables using modern Python code. Apply the Law of Large Numbers and Central Limit Theorem to simulated data. Model complex scenarios using practical Monte Carlo simulation techniques. The material begins with basic definitions and foundational theory before walking through practical code simulations and key limit theorems. Designed for beginners in programming, data analysis, or computer science, no prior background in advanced statistics is required. Begin reading today to build a strong practical foundation in probability.