• Text book.
  "Fundamentals of Probability with stochastic processes"
  Saeed Ghahramani, Pearson Prentice Hall (third edition).


• Lecture notes.  Lecture notes for the course are available from the link. These contain the theoretical results and proofs that we will go through in class. They are no substitute for class attendance. More details and examples will be provided in class.


• Recommended texts.
  "A first course in probability" Sheldon M. Ross.
  "Introduction to probability models" Sheldon M. Ross
  "Probability and random processes" Geoffrey R. Grimmett and David R. Stirzaker
  "Probability and random processes, problems and solutions" Geoffrey R. Grimmett and David R. Stirzaker
  


• Academic Honesty.   All students must be honest and forthright in their academic studies. Students are expected to do their own work and neither give nor receive unauthorized assistance. Any violation of this standard must be reported to the Office of Judicial Affairs. Know the University’s Policy on Academic Dishonesty found in the Student Guide to University Policies. Copies of it may be obtained on the Web at http://www.udel.edu/stuguide/08-09, in the University Advisement Center (102 Elliott Hall ), or in the Office of Judicial Affairs (218 Hullihen Hall). For all other administrative questions/problems see your home department.

Syllabus

Basic notions of probability, combinatorial and counting methods, tree diagrams, conditional probability, independent events, Bayes' Formula, random variables, discrete and continuous probability distributions, joint distributions, expectation and conditional expectation, independence of random variables, variance, covariance and standard deviation, moments, generating functions, moment and characteristic functions, inequalities, limit theorems, central limit theorem, law of large numbers, notions of convergence, basics of Poisson processes and simulation.

Back to top

Prerequisites

MATH210 or MATH230, and MATH243 (corequisite).
This course assumes proficiency in (multivariate) calculus and differentiation and some basic knowledge of algebra and analysis such as on sums and series. Please check if your background and knowledge is adequate with the prerequisite assignment sheet.

Back to top

Grading

Weekly PROBLEM SETS,  TWO MIDTERMS, and a FINAL will determine your grade for the course.  The weighting for these are discussed in more detail below. 

NO MAKE-UP MIDTERMS WILL BE GIVEN.   If you miss a midterm exam due to legal reasons (you will need proof for this) the final exam will count for that exam also.  

• PROBLEM SETS (20%).  Problems sets will be assigned weekly, see assignments below.


• EACH MIDTERM (20%).  The midterms are tentatively scheduled for Wednesday 10/01/08 (Class 13) and Wednesday 11/05/08 (Class 28). The problems on the exam will be on a similar level and nature as the homework problems. As for the solutions to your problem sets, clear explanations of your steps and a consistent argument will be essential for full credit.   


• FINAL (40%):  The date of the final exam will be announced later in the semester. You will need to write the final exam for successful completion of the course.   
  

Assignments

• Problem sets   These are assigned on Friday of each week. Your solutions are due the following Friday. Only selected problems will be corrected and graded. The graded homework problems may sometimes be a bit more challenging than the practice homework problems, and will require you to apply the concepts that you have learned. Please note that credit will only be given to solutions that include clear explanations of your steps and a consistent argument. Barring some exceptions like serious illness late homework will not be accepted. While I encourage you to work together and discuss the material and homework, the solutions to the problem sets that you hand in will have to be your own, in your own words.

First assignment (for some extra credit) (due Friday 9/5/08) Complete prerequisite assignment sheet.

Problem set 1 (due Friday 9/12/08) Chapter 1: Section 1.2   10, 14  Section 1.4   4, 10, 18, 22   Honors: Section 1.7   12

Problem set 2 (due Friday 9/19/08) Chapter 1: Section 1.7   4,   Review   8 ,   Chapter 2: Section 2.2   10,15,16,   Section 2.3   8,12   Honors: Section 2.2   23,   Section 2.3   26

Problem set 3 (due Friday 9/26/08) Chapter 2: Section 2.4   14,   16,   18,   20   Chapter 3: Section 3.1   4,   9   Honors: Section 2.4   34,   38  

Problem set 4 (due Friday 10/3/08) Chapter 3: Section 3.2   5,   6   Section 3.3   8   Section 3.4   2   ,11   Section 3.5   26 Honors: Section 3.3   14   Section 3.4   15  

Problem set 5 (due Friday 10/10/08) Chapter 3: Section 3.5   16,   24,   28   Review   19   Chapter 4: Section 4.2   7   ,16   Honors: Chapter 3: Section 3.5   43  

Problem set 6 (due Friday 10/17/08) Chapter 4: Section 4.3   5,   10   Section 4.4   4   9,   11  Section 4.5   8   Honors: Chapter 4: Section 4.3   12   Section 4.4   15  


• Practice homework   These problems are for you to practice and get a good understanding of the material covered in class. Practice homework will not be handed in or graded. A list of practice problems and sample solutions for each chapter will be made available below.
  
  Chapter 1: Section 1.2   2,4,6,8   Section 1.4   1,3,7,9,19  Section 1.7   1,5,10
  Sample solutions for chapter 1
  
  Chapter 2: Section 2.2   1,3,5,8,9,11,17  Section 2.3   2,6,10  Section 2.4   1,3,5,11,13,15,21,39
  Sample solutions for chapter 2
  
  Chapter 3: Section 3.1   1,3,5,11  Section 3.2   1  Section 3.3   1,3,7  Section 3.4   1,4,8,10  Section 3.5   4,6,8,11,17,19,27,29,36,37
  Sample solutions for chapter 3
  
  Chapter 4: Section 4.2   1,5,11  Section 4.3   1,3,7,13  Section 4.4   3,5,7  Section 4.5   1,3,5,7  Section 4.6   1
  Sample solutions for chapter 4
  
  
  
  
• Honors section   Extra homework problems will be assigned for honors students. In addition, each honors student will complete a homework project (towards the end of the semester) on material that we will not cover in class and make a presentation on this project to the honors section.
  
  
  

Divertissements