Probability I

Probability spaces. Random variables and vectors. Probability distributions and distribution functions in Rn. Stochastic independence. Expected value of random variables: basic properties and inequalities, convergence theorems. Conditional distribution and expectation: existence theorems and regularization. Laws of large numbers: weak law, Borel-Cantelli lemma, strong law. Theorems of one, two and three series. Characteristic functions and convergence in distribution on Rn. Lindeberg-Feller theorem.

References:
CHUNG, K. L. – A Course in Probability Theory, 2nd ed. New York, Academic Press, 1974.
FELLER, W. – An Introduction to Probability Theory and its Applications, Vol. II, 2nd ed., New York, John Wiley & Sons, 1966.
SHIRYAYEV, A. N. – Probability. New York, Springer-Verlag, 1984.
VARADHAN, S.R.S. – Probability Theory, New York, Courant Institute of Mathematical Sciences, 2001.

* Standard program. The teacher has the autonomy to make any changes.