This course will first cover Kolgomorov's axioms of probabilities, basics of set theory, discrete combinatorial probability, Bayes' theorem, probability distributions and their properties and assumptions of dependence and independence, followed by the foundational topics of statistics: sampling distributions, the law of large numbers and the central limit theorem. This course will mix theoretical approaches with simulation-based illustrations of these main topics. The student will solve via analytical and simulation based approaches in statistical programming language R.
