**Important Dates: **Last day for Automatic Withdrawal: Wednesday, October 26. Exam 1: Monday, October 3. Exam 2: Monday, November 7. Final Exam: 10:15 a.m.-12:15 p.m., Monday, December 12.

** Religious Holiday Policy:** If you will miss class, especially a class during which there will be an exam or other required work, for a religious holiday, you must inform me during the first two weeks of the semester.

**Cheating:** It is not possible to cheat on homeworks. All exams must be your own individual work. All suspected cases of cheating will be handled in accordance with University procedures found at http://dsa.indiana.edu/ethics.html . If you do cheat, you will receive an F* in the course - the star informs the registrar that the F is due to cheating. Additional sanctions may be imposed by the Dean.

** Homework:** There will be 11 homework assignments throughout the term. See the schedule below. A star (*) on a problem indicates that a hint to the problem appears in the back of the text. One assignment will be dropped from the calculation for your homework average.

** Grades:** Grades are calculated as 40% Homework, 15% Exam 1, 15% Exam 2, 25% Final Exam, 5% Attendance and Participation.

## Tentative Syllabus | ||
---|---|---|

Date | Lecture Topics | Section |

Monday, August 29 | length, dyadic intervals, Rademacher functions, step functions, Chebyshev's inequality for step functions, weak law of large number. | Section 1 |

Wednesday, August 31 | Negligible sets, strong law of large numbers, normal numbers, length | Section 1 |

Friday, September 2 | Sets, fields, sigma-fields, probability measure | Section 2 |

Homework 1: (due Wednesday, Sept. 7) 1.1*, 1.2, 1.3*, 1.8, 2.1 | ||

Monday, September 5 | Labor Day Holiday | -- |

Wednesday, September 7 | Lebesgue meaure, cylinder sets, outer measure | Sections 2-3 |

Friday, September 9 | Existence and uniqueness | Section 3 |

Homework 2: (due Monday, September 12) 2.3*, 2.5*, 2.11*, 2.13, 2.20 | ||

Monday, September 12 | conditional probability, limit sets, independence | Section 4 |

Wednesday, September 14 | subfields, Borel-Cantelli lemmas | Section 5 |

Friday, September 16 | Zero-One law, simple random variables | Sections 4-5 |

Homework (due Monday, September 19) 3.5, 3.11, 4.2(a), 4.6, 4.11 | ||

Monday, September 19 | convergence, independence | Section 5 |

Wednesday, September 21 | Expected value | Section 5 |

Friday, September 23 | Law of large numbers | Section 6 |

Homework 4: (due Monday, September 26) 5.3 (assume X is simple), 5.5*, 5.12 (assume X is discrete but not necessarily simple), 6.4, 6.6 | ||

Monday, September 26 | gambler's ruin, gambling strategies | Section 7 |

Wednesday, September 28 | gambling strategies | Section 7 |

Friday, September 30 | introduction to Markov chains | Section 8 |

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Monday, October 3 | Exam 1 (Covering sections 1-6) | |

Wednesday, October 5 | transience and persistence | Section 8 |

Friday, October 7 | stationary distributions | Section 8 |

Homework 5: (due Monday, October 10) 7.2, 7.4, 7.7*, 8.2, 8.3 | ||

Monday, October 10 | moment generating functions, large deviations | Section 9 |

Wednesday, October 12 | Law of the Iterated Logarithm | Section 9 |

Friday, October 14 | general measures | Section 10 |

Homework 6: (due Monday, October 17) 8.15, 8.19*, 8.24*, 8.25*, 9.4 | ||

Monday, October 17 | outer measure | Section 11 |

Wednesday, October 19 | measure in Euclidean space | Section 12 |

Friday, October 21 | measurable functions | Section 13 |

Homework 7: (due Monday, October 24) 10.4, 11.2, 12.12, 13.1, 13.8 | ||

Monday, October 24 | distribution functions | Section 14 |

Wednesday, October 26 | weak convergence | Section 14 |

Friday, October 28 | integration | Section 15 |

Homework 8: (due Monday, October 31) 14.1, 14.2, 14.3*, 14.5*, 15.1* | ||

Monday, October 31 | properties of integration: monotonicity, linearity, limits | Section 16 |

Wednesday, November 2 | densities and changing variables | Section 16 |

Friday, November 4 | uniform integrability | Section 16 |

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Monday, November 7 | Exam 2 (Covering sections 1-14) | |

Wednesday, November 9 | integration with respect to Lebesgue measure | Section 17 |

Friday, November 11 | product measure and Fubini's Theorem | Section 18 |

Homework 9: (due Monday, November 14) 16.7, 16.8*, 16.9*, 17.4, 17.5 | ||

Monday, November 14 | integration by parts | Section 18 |

Wednesday, November 16 | random variables and distributions | Section 20 |

Friday, November 18 | independence and sequences | Section 20 |

Homework 10: (due Monday, November 21) 18.4, 18.7, 18.14, 20.5, 20.6 | ||

Monday, November 21 | convolution and convergence in probability | Section 20 |

Thanksgiving Break | ||

Monday, November 28 | expected value, moment generating functions | Section 21 |

Wednesday, November 30 | sum of independent random variables, strong law, weak law, moment generating functions, 0-1 law. | Section 22 |

Friday, December 2 | maximal inequalities, convergence | Section 22 |

Homework 11: (due Monday, December 5) 20.20*, 21.7, 21.10*, 21.21*, 22.8* | ||

Monday, December 5 | exponential distribution and Poisson processes | Section 23 |

Wednesday, December 7 | Poisson processes | Section 23 |

Friday, December 9 | Summary and evaluations | |

Final Exam: Monday, December 12 at 10:15 am in SW 221 (Covering sections 1-22) |