Probability Theory: Discrete Probability Space, Axioms of Probability, Discrete Random Variables, Distributions and Discrete Density (Uniform, Bernoulli, Binomial, Poisson), Identically Distributed Random , Independence, Expectation, Moments, Covariance, Variance, Sum of Random Variables, Continuous Random Variables, Cumulative Distribution Function (Uniform, Exponential, Gaussian), Weak and Strong Law of Large Numbers, Monte Carlo Integration, Central Limit Theorem.

Statistics: Review of Bernoulli, Binomial, Normal, Chi-squared and Student distributions, Descriptive statistics (Population, Samples, Types of Variables, Measures of Central Tendency, Measures of Variability and Measures of Shape), Sampling Statistics, Confidence Intervals (for Mean, Variance, Difference between Mean Parameters), Markov Chains from an Algebraic Viewpoint, Examples (Birth and Death, Cellular automata and SIR), Markov Chains as Stochastic Processes, Examples and links with continuous systems.

(1) Achim Klenke, Probability Theory, 3rd Edition, Springer

(2) Sheldon Ross, A First Course in Probability, 5th Edition

(3) Ross, Introduction to Probability And Statistics for Engineers And Scientists, 3rd Edition