Probability: Basic concepts, conditional probability.

Random variables: Definitions density and distribution functions, expectation, variance, covariance, correlation, transformations, sums, generating functions, characteristic functions, conditional laws.

Discrete and continuous laws: Bernoulli, binomial, hypergeometric, Poisson, geometric, normal, exponential, Gamma, Cauchy, Weibull, Gumbel, chi-square.

Limit theorems: law of large numbers, central limit theorem

Introduction to statistics: frequentist, Bayesian viewpoints

Estimation: point estimation, bias, mean square error, maximum likelihood estimator

Hypothesis testing: errors, power, significance, chi^2