Sevak Mkrtchyan

7121 Wean Hall

e-mail: sevakm (at_sign) andrew.cmu.edu

25% - Homework assignments

20% - Midterm exam 1 (Monday, October 1, in class)

20% - Midterm exam 2 (Monday, November 5, in class)

35% - Final exam

You are allowed to collaborate on homework assignments, however writing up of the solutions should be done individually. You should never share written down solutions which will be submitted as homework by other students.

This is a schedule for what I have covered and what I plan to cover in class each day. This section will be updated regularly during the semester.

Date |
Topic |
Homework |
Due |

Mon, August 27 | Introduction. The sample space. | Chapter 1.8: 4,16; | Sep 5 |

Wed, August 29 | Probabilities. | Chapter 2.10: 1,3,4,5,11,15. | Sep 5 |

Fri, August 31 | Combinatorial Analysis | ||

Mon, September 3 | Labor day; No classes | ||

Wed, September 5 | Combinatorial Analysis, Binomial series | Chapter 2.10: 17, 19, 27, 32, 38 | Sep 12 |

Fri, September 7 | Hypergeometric distribution | Chapter 2.11: 3,5,6 | Sep 12 |

Mon, September 10 | Waiting times | Chapter 2.10: 35,36 | Sep 19 |

Wed, September 12 | Random walks | Chapter 3.10: 1,2,3,4 | Sep 19 |

Fri, September 14 | Random walks - the reflection principle | Part of homework 3 | Sep 19 |

Mon, September 17 | Random walks - first and last return probabilities | Chapter 3.10: 6,7,11,12 | Sep 26 |

Wed, September 19 | Random walks - steps on the positive side, maxima | ||

Fri, September 21 | Combination of events, Conditional probability | Chapter 4.6: 3,8,12,15 | Sep 26 |

Mon, September 24 | Stratified populations, Independence | Chapter 5.8: 2,6,7,15,16, | Oct 5 |

Wed, September 26 | Binomial distribution, law of large numbers | Chapter 6.10: 3,5,6 | Oct 5 |

Fri, September 28 | Poisson distribution, Poisson process | ||

Mon, October 1 | Midterm 1 | ||

Wed, October 3 | Normal distribution | Chapter 6.10: 11,12,17,20,23,27,41 | Oct 17 |

Fri, October 5 | Expectation, variance, standard deviation | Part of homework 6 | Oct 17 |

Mon, October 8 | More on the normal distribution | ||

Wed, October 10 | Midterm exam overview | ||

Fri, October 12 | DeMoivre-Laplace limit theorem | ||

Mon, October 15 | Examples; Normal approximation to the poisson distribution | ||

Wed, October 17 | Large deviations | Chapter 7.7: 2,4,5,7,9,12,13,14 | Oct 26 |

Fri, October 19 | Mid-Semester Break; No Classes | ||

Mon, October 22 | Infinite Bernoulli trials | ||

Wed, October 24 | Borel-Cantelli Lemmas | Part of homework 8 | Nov 2 |

Fri, October 26 | Strong law of large numbers | Chapter 8: 1,2,3,4,5,6 | Nov 2 |

Mon, October 29 | Conditional distribution and conditional expectation | Extra credit problem (Blackboard) | Nov 9 |

Wed, October 31 | Joint distribution | Part of homework 9 | Nov 9 |

Fri, November 2 | Covariance | Chapter 9: 2,8,9,10,21,34 | Nov 9 |

Mon, November 5 | Midterm 2 | ||

Wed, November 7 | The weak law of large numbers | Chapter 10:1,2ab,6,8 | Nov 16 |

Fri, November 9 | Absolutely continuous random variables | Part of homework 10 | Nov 16 |

Mon, November 12 | Joint density, marginals, conditional expectation | ||

Wed, November 14 | The partition theorem | ||

Fri, November 16 | Transformed random variables | Homework 11 | Nov 30 |

Mon, November 19 | The multivariate normal distribution | ||

Wed, November 21 | Thanksgiving Holiday; No Classes | ||

Fri, November 23 | Thanksgiving Holiday; No Classes | ||

Mon, November 26 | Generating functions | ||

Wed, November 28 | Characteristic functions | ||

Fri, November 30 | Proof of the Central Limit Theorem. Brownian Motion | Homework 12 | Dec 7 |

Mon, December 3 | Brownian Motion | ||

Wed, December 5 | Brownian Bridge | ||

Fri, December 7 | Construction of a Poisson process |

You are expected to attend every class and arrive on time. It is your responsibility to be informed of any announcements made in class.