**Fall 2013 course**

**Stat 6344 - PROBABILITY THEORY I**

Time: | MW 9:30 - 10:45 am |
Room: | FO 2.404 | Instructor: | Michael Baron |

Time: | MW 9:30 - 10:45 pm |

Room: | FO 2.404 |

Instructor: | Michael Baron |

Office: | FO 2.602-E |

Phone: | 972-UTD-6874 |

Office hours: | Monday, Wednesday 4:15 - 5:15 pm |

Text: | Probability by A. N. Shiryaev, 2nd Edition, |

Springer series "Graduate Texts in Mathematics", 1995. ISBN 0-387-94549-0 | |

- Introduction and axioms. Probability models with finitely many and infinitely many outcomes.
- Bernoulli Scheme. Local and Integral theorems.
- Random variables. Laws of large numbers. Large deviations.
- Conditional probability, conditional expectation. Martingales.
- Markov stopping times and Optional Stopping Theorem.
- Probability measures on measurable spaces. Caratheodori's Theorem.
- Distributions and moments. Kolmogorov's Zero-One Law. Maximal inequalities.
- Convergence of probability measures.
- Characteristic functions. Central limit theorem. Kolmogorov's Zero-One Law.
- Applications.

Prerequisite: |
MATH 5302 (Mathematical Analysis II) or equivalent |

**Grading:**

Homework | 10% | Homework will be assigned every week. A serious and steady effort to work out all the homework problems is highly recommended. |

Quizzes | 30% | Short weekly quizzes closely related to the material of the latest homework assignment. Quizzes are closed-book; one cheat-sheet is allowed. |

Midterm exam | 25% | A 1 1/4-hour midterm covers chapters 1-2. |

Final exam | 40% | A 2 1/2-hour final exam covers chapters 4-6 but it is cumulative indirectly. Exams are open-book, -notes, etc. |

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Call: | (972)-UTD-6874 | Write: | mbaron@utdallas.edu | Click: | www.utdallas.edu/~mbaron/ |