Statistics

This course studies probability theory, which is a branch of mathematics that deals with modeling uncertainty. This is important because of its direct applications in areas such as genetics, finance, data science and telecommunications. It also forms the fundamental basis for many other fields in the mathematical sciences including statistics, modern optimization methods, and risk modeling. This course provides an introduction to the theory of probability and random variables. The topics covered are: axioms of probability, conditional probability; Bayes’ theorem; discrete random variable, moment, bound probability, probability generating function, standard discrete distribution; continuous random variable, uniform, normal, Cauchy, exponential, gamma and chi-square distribution, transformation, Poisson process; bivariate distribution, marginal and conditional distribution, independence, covariance and correlation, linear combination of two random variables, bivariate normal distribution; sequence of independent random variables, weak law of large numbers, central limit theorem; probability transition matrix; method for solving equilibrium equations.