Probability

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

Workload

45 hours

**Mandatory: **

- 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;

**Complementary: **

- 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;