Statistics for Postgraduate Exams: Random Variables and Distributions

Preparing for postgraduate statistics entrance exams requires a rock-solid grasp of core probability concepts and mathematical frameworks. This comprehensive written course is designed to take you from foundational theory to exam-ready problem-solving confidence. You will build a deep, intuitive understanding of how variables behave and how to model real-world data mathematically. By working through clear explanations and structured written exercises, you will develop the analytical skills needed to tackle challenging exam questions with precision. What you'll learn: Understand core probability foundations and the mathematical definition of random variables; Master univariate random variables, including cumulative distribution functions and probability density functions; Calculate mathematical expectation, variance, moments, and moment-generating functions with accuracy; Analyze standard discrete distributions such as Binomial, Poisson, and Geometric; Analyze standard continuous distributions including Normal, Exponential, and Beta; Apply theoretical statistical properties to solve exam-style algebraic and calculus-based problems. The course begins with essential terminology and fundamental probability concepts before guiding you systematically through discrete and continuous variables, culminating in the practical application of standard distributions. This course is designed for students and graduates preparing for postgraduate statistics entrance examinations, requiring only a basic background in algebra and introductory calculus. Start reading today to master the mathematical foundations of statistics and secure your academic future.