Probabilities

Probabilities on a continuous universe: random variable, distribution function, density, moments (expectation, variance), independence of two random variables, Markov and Bienaymé-Tchebychev inequalities
Usual continuous laws: uniform on a segment, exponential, normal, Gaussian, convergence in law, limit central th, law approximation (Binomiale by Normal, Poisson by Normal), continuity correction. or pairs of v.a.
Probabilities on a countable universe definition of probability space, events, independence of events, conditional probabilities, compound probability formula, total probability formula, Bayes formulas, discrete random variables, law of a random variable, expectation, transfer theorem, variance, we deal directly with the countable case. Usual discrete laws: discrete uniform law (equidistributed law), binomial law including Bernoulli's law, Poisson's law and geometric law.