Concise Probability Theory Summary – Random Variables & Distributions (Unit II & III)

These notes provide a concise summary of key concepts in Probability Theory, focusing specifically on Unit II and Unit III topics. Unit II covers the fundamentals of random variables, including discrete and continuous random variables, moments, moment generating functions, cumulative distribution functions, and brief derivations of standard distributions such as Binomial, Poisson, Uniform, Exponential, and Normal distributions, along with functions of a random variable . Unit III introduces two-dimensional random variables, with summarized explanations of joint, marginal, and conditional distributions, covariance, correlation, linear regression, transformation of random variables, and the Central Limit Theorem for independent and identically distributed variables. The content is exam-oriented and revision-focused, making it suitable for quick review before semester exams, rather than as a full textbook replacement.