Theory of Statistics I - Introduction to Probability & Distribution Theory

This course emphasizes the mathematical theory of probability and statistics. Students are expected to have a working knowledge of topics including axioms of probability, independence, conditional probability and Bayes' theorem, data generating processes, random variable and their distribution. Some of the probability distributions developed are binomial, Pascal exponential. Poisson, gamma, normal and multivariate. Other topics considered include t, X , F, Erlang and Weibull distributions, central limit theorem, generating functions, law of large numbers, random sampling distributions, introduction to stochastic processes and their application to the construction of statistical models. Those aspects useful in statistical applications will be emphasized.