Probability and Univariate Distributions for Mathematical Statistics

Mastering probability is the single most important step toward succeeding in rigorous mathematical statistics exams and understanding modern data science. This text-based course guides you from the absolute basics of probability theory to the complex behaviors of univariate distributions, giving you the theoretical depth and problem-solving skills needed for competitive academic assessments. What you'll learn: - Understand fundamental probability concepts, sample spaces, and conditional probability. - Master discrete and continuous random variables alongside cumulative distribution functions. - Analyze standard univariate distributions including Binomial, Poisson, Normal, and Exponential. - Calculate mathematical expectation, variance, moments, and moment-generating functions. - Apply transformation techniques to find the distribution of functions of random variables. - Connect theoretical probability distributions to modern data science and statistical modeling applications. You will start with core definitions and axioms before moving systematically through random variables, expectation, and specific probability distributions, practicing with detailed written explanations and step-by-step mathematical proofs. Designed for students preparing for mathematical statistics exams and analytical professionals seeking a rock-solid theoretical foundation. No advanced prerequisites are required, though basic calculus is helpful. Begin reading today to build a flawless understanding of univariate probability distributions.