- Instructor: Mikhail Ershov
- Office: Kerchoff 302
- e-mail: ershov
*at*virginia*dot*edu - Office hours: 3 hrs TBA and by APPOINTMENT
- Course webpage:
*http://people.virginia.edu/~mve2x/3100_Spring2016*

- required text:
*Introduction to Probability*, second edition, Dimitri Bertsekas and John Tsitsiklis - additional text (recommended):
*Elementary Probability for Applications*, Rick Durrett - additional text (recommended):
*Probability*, Jim Pitman

It is not expected that you have taken a proof-based course prior to 3100 and this course will not emphasize abstract proofs, but there will be some theoretical questions in both exams and homeworks.

week | sections | topics |

Jan 21 | 1.2 | Probabilistic models. |

Jan 26, 28 | 1.3, 1.4 | Conditional Probability. Bayes' Rule |

Feb 2, 4 | 1.5, 1.6 | Independence. Counting. |

Feb 9, 11 | 2.1, 2.2, 2.3 | Discrete Random Variable. Probability Mass Functions (PMF). Functions of Random Variables. |

Feb 16, 18 | 2.4, 2.5 | Expectation, Mean and Variance. Joint PMFs |

Feb 23, 25 | 2.6, 2.7 | Conditioning and independence for discrete random variables. |

Mar 1 | 3.1 | Continuous Random Variables and PDFs. |

Mar 15, 17 | 3.2, 3.3 | Cumulative Distribution Functions. Normal Random Variables. |

Mar 22, 24 | 3.4, 3.5 | Joint PDFs and Conditioning for Continuous Random Variables. |

Mar 29, 31 | 4.1, 4.2, 4.3 | Derived Distributions. Covariance and Correlation. Conditional Expectation and Variance Revisited. |

Apr 5,7 | 5.1, 5.2, 5.3 | Markov and Chebyshev Inequalities. The Weak Law of Large Numbers. Convergence in Probability. |

Apr 12,14 | 5.4, 5.5 | The Central Limit Theorem. The Strong Law of Large Numbers. |

Apr 19, 21 | 6.1 | The Bernoulli Process. |

Apr 26, 28 | 6.2 | The Poisson Process. |

May 3 | Review. |

- homework: 15%
- quizzes: 15%
- midterm: 20%
- final: 50%

- Midterm exam: Thu, Mar 3rd
- Final exam: Sat, May 7th, 9am-12pm

- Homework will be assigned weekly but only about half of the assignments will be collected
- For homework assignments that will be collected 3-4 selected (but not announced in advance) problems will be graded for credit.
- During most weeks when assigned homework will NOT be collected, a 15-25 minute long quiz will be given at the beginning of class on the day when homework is due (usually Thursday). Most quiz questions will either come directly from homework or will be similar to homework problems; however, I may also ask for formulations of definitions and theorems on the current material. Tentative quiz dates are Feb 4, Feb 25, Mar 24, Apr 7, Apr 21 and May 3 (all Thursdays except May 3).
- Please STAPLE your homework.
- No late homework will be accepted. However, the lowest homework score (out of about 6 assignments) will be dropped.
- The lowest quiz score (out of about 6 quizzes) will be dropped.

- If you miss an exam or quiz without a compelling reason, you will
be assigned the score of
**0**on that exam/quiz. - If you miss an exam for a legitimate reason (and appropriate documentation is provided), a make-up will be arranged; however, you must obtain my permission for a make-up before the exam, except for emergencies
- If you miss a quiz for a legitimate reason (and appropriate documentation is provided): for the first missed quiz no make-up will be given, but that quiz will not be counted towards your score; for subsequent misses the same rules as for exams will apply.
- University regulations specifically prohibit early make-ups.

- You are welcome (and even encouraged)
to work on homework together, but you
*must*write up solutions independently, in your own words. In particular, you**should not be consulting others during the process of writing down your solution**.

- Monday, February 3 -- Last day to ADD a course, elect the audit option, change the grading option (grade or CR/NC), or establish an independent study
- Tuesday, February 4 -- Last day to DROP a course (deletion from the transcript)
- Wednesday, March 16 -- Last day to withdraw from a course