Probability

e-mail: laurentiu.maxim@lehman.cuny.edu
office hours: Thu, 3-6 PM, Room G 100B.

CLASS SCHEDULE: Tue, Thu, 7:50-9:30 PM, Room G227.

CLASS HOMEPAGE: http://comet.lehman.cuny.edu/maxim/Probability.html

DESCRIPTION:

Basic probability theory. Combinatorial problems, distributions, expectation, law of large numbers and central limit theorem, Bernoulli processes and Markov chains. Other topics from probability and statistics.

TEXTBOOK:

Probability
Jim Pitman, Springer.

PREREQUISITE: MAT 176.

FINAL EXAM: Thu, December 18, 8-10PM.

GRADE: 10 Quizzes: 5% each, Midterm: 20%, Final Exam: 30%.

THE QUIZES COUNT MORE TOWARDS THE GRADE THAN EITHER OF THE EXAMS! Students must submit completed homework from the prior week in order to begin a quiz and that homework will be part of the score. Students who miss quizes because they are absent, late or have not completed the homework will receive a 0 on that quiz. There will be no make up quizes.

In the following syllabus, homework is written below the lesson when it is assigned and should be completed before the next meeting. All quizes and homework collection are on Tuesdays.

SYLLABUS (updated regularly):

• Lesson 1: Section 1.1 - Basic Probability concepts.
  HW: Section 1.1: solve 1, 3, 4, 7, 9. Read Section 1.2.
• Lesson 2: Section 1.3 - Distributions.
  HW: Section 1.3: solve 1, 2, 4, 7, 8, 11, 14.
• Lesson 3: Section 1.4 - Conditional probability and independence.
  HW: Section 1.4: solve 1, 2, 3, 4, 5, 6, 7, 8.
• Lesson 4: Section 1.5 - Bayes' Rule and Quiz 1.
  HW: Section 1.5: solve 1, 2, 3, 4, 5, 7.
• Lesson 5: Section 1.6 - Sequence of events.
  HW: Section 1.6: solve 1, 3, 5, 7; Read Example 3 on page 60; Read the Summary on pages 72-73.
• Lesson 6: Section 2.1 - The Binomial Distribution and Quiz 2.
  HW: Section 2.1: 1, 2, 4, 5, 7.
• Lesson 7: Section 2.2 - The Normal Distribution.
  HW: Section 2.2: 1, 3, 4, 5, 8.
• Lesson 8: Section 2.4 - The Poisson Distribution and Quiz 3.
  HW: Section 2.4: 2, 5, 6.
• Lesson 9: Section 2.5 - Random Sampling and Quiz 4.
  HW: Section 2.5: 1, 2, 3, 6, 7, 8; Read the Summary on pages 130-131.
• Lesson 10: Section 3.1 - Intro to Random variables.
  HW: Section 3.1: 1, 2, 3, 4, 5.
• Lesson 11: Section 3.1 - Intro to Random variables, (continued) and Quiz 5.
• Lesson 12: Section 3.2 - Expectation.
  HW: Section 3.2: 1, 3, 4, 6, 7, 8.
• Lesson 13: Section 3.2 - Expectation (continued) and Quiz 6.
  HW: Section 3.2: 9, 10, 11, 12, 13.
• Lesson 14: Section 3.4 - Discrete distributions.
  HW: Section 3.4: 1, 2, 3, 5, 6, 7.
• Lesson 15: Section 3.3 - Standard Deviation and Quiz 7.
  HW: Section 3.3: 1, 2, 5, 7, 12, 13.
• Lesson 16: Section 4.1 - Probability Densities.
  HW: Section 4.1: 1, 2, 3, 4, 5, 6, 7, 13.
• Lesson 17: Section 4.2 - Exponential Distributions and Quiz 8.
  HW: Section 4.2: 1, 3, 4, 5, 6.
• Lesson 18: Section 4.4 - Change of variables.
  HW: Section 4.4: 1, 3, 4, 5, 10.
• Lesson 19: Section 4.5 - Cumulative Distribution Functions and Quiz 9.
  HW: Section 4.5: 1, 2, 3, 4, 5, 8(a,b).
• Lesson 20: Sections 5.1 and 5.2- Continuos Joint Distributions: uniform distributions, densities, and Quiz 10.
  HW: Section 5.1: 1, 2, 3, 4, 6, 9; Section 5.2: 1, 2, 3, 4, 5, 6.
• Lesson 21: Section 6.1 - Conditional Distributions: discrete case.
  HW: Section 6.1: TBA.