Program (ay 2017/18)

Revision of probability: probability space; conditional probability (total probability formula and Bayes formula). Random variables. Expectation and variance. Chebyshev inequality.
Discrete r.v.: the mass function. Bernoulli, binomial, Poisson, geometric, hypergeometric, negative binomial distributions. Joint mass function; marginal mass functions. The distribution of X+Y.
Continuous r.v.: the distribution function and the density function. Uniform, exponential, normal distributions. The joint density function; the marginal density functions. Transformation of random variables: Y=aX+b, Y=X².
Law of large numbers. Central limit theorem.

Normal random vectors: the expectation vector and the covariance matrix. Linear transformations of a normal random vector.

Sequence of events: how to compute probabilities. Borel-Cantelli lemmas (with proofs). Example: gambling systems.