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AMS 569, Probability Theory I
Probability spaces and sigma-algebras. Random variables as measurable mappings. Borel-Cantelli lemmas. Expectation using simple functions. Monotone and dominated convergence theorems. Inequalities. Stochastic convergence. Characteristic functions. Laws of large numbers and the central limit theorem. This course is offered as both AMS 569 and MBA 569. 
PrerequisiteAMS 510
3 credits, ABCF grading 

Spring Semester

Required Textbook:
"Probability Essentials" by Jean Jacod and Philip Protter; 2nd edition (corrected second printing 2004); Springer;
ISBN: 978-3-540-46871-8 

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