Foundations of Probability and Statistical Distributions

Data-driven decisions rely heavily on understanding risk, uncertainty, and variability. To make sense of complex data, you must first grasp how random events behave and how statistical models describe the real world. This course takes you from the absolute basics of probability to a firm understanding of how different distributions model real-life scenarios. You will start by learning foundational terminology, set theory, and the core axioms of probability. From there, you will explore random variables, expectation, variance, and the most common discrete and continuous distributions. To keep your skills modern, you will also learn how these mathematical concepts form the basis of modern machine learning algorithms and data science models. What you'll learn: - Understand foundational probability concepts, sample spaces, and events - Calculate conditional probabilities and apply Bayes' theorem to real-world scenarios - Define discrete and continuous random variables and calculate their expected values - Analyze key discrete distributions including Binomial, Poisson, and Geometric - Evaluate continuous distributions such as Normal, Exponential, and Uniform - Apply the Central Limit Theorem to understand sample behaviors in modern data analysis This text-based course guides you step-by-step through clear explanations, logical proofs, and practical written exercises. You will build your knowledge progressively, starting with simple coin-toss examples and ending with complex probability density functions. This course is designed specifically for beginners, students, and aspiring data professionals who want a solid mathematical foundation. No prior background in advanced statistics is required. Start reading today to build a strong mathematical foundation for your data journey.