Probability

Basic information

Workload: 

45 hours

Syllabus: 

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.

Bibliography

Mandatory: 

•    James, Barry. Probability: An intermediate level course. IMPA. 2004; 
•    Blitzstein, Joseph and 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 and Schervish, Mark. Probability and statistics. 4th ed. 2011 
•    Williams, David. Probability with Martingales. Cambridge University Press, 1991;