Basic topics: Sample space, random variables, hope, transformations and limit theorems (law of large numbers and central limit theorem). Advanced topics: basic results of the measurement theory, changes in order between limits and hopes, normal multivariate distribution, conditional distribution and hope.

Basic Information

45 hours


  • James, Barry. Probabilidade: Um curso em nível intermediário. IMPA. 2004;
  • Blitzstein, Joseph &  Hwang, Jessica. Introduction to Probability. 2014;
  • Grimmett, Geoffrey, and David Stirzaker. Probability and Random Processes. 3rd ed. Oxford University Press, 2001;


  • Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena Scientific, 2008;
  • DeGroot, Morris & Schervish, Mark. Probability and Statistics. 4th ed. 2011
  • Williams, David. Probability with Martingales. Cambridge University Press, 1991;