Welcome to the Course Page of

MATH 2030 3.00 A

Elementary Probability

Summer 2013

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Department of Mathematics and Statistics
York University
4700 Keele Street
Toronto, Ontario M3J 1P3

Course Organization:


Course Information

Course Schedule


Exams Information

Links & Other Resources


This area will contain announcements and solutions to quizzes and midterm exam. Announcements made in class will be posted here in reverse chronological order and will not be repeated in class. Please take a minute to read the announcements carefully, as they often get updated. You may need to Reload/Refresh this page.


June 27:

Please click here to see your final exam mark and unofficial


letter grade for the course. Also, please note that your official


grade for the course will be sent to you by the Registrar's


Office upon the approval by the faculty.



June 19:

Please click  here  to see your term scores for the course.


Please note that both tests will be counted out of 50.

June 18:

As it was announced in the last class, I am making available the final


exam formula sheet.

June 15:

I am making available  solutions  to Homework problems from


Sections 2.4 and 3.5.

June 14:

As it was announced in the class yesterday, the Final Examination


for the course will take place on Thursday, June 20, from 19:00 to


22:00 in CLH D.


The exam will be comprehensive, covering the entire course material


that we covered in class from Appendix 1, Sections 1.1-1.6, 2.1, 2.2


2.4, 2.5, 3.1-3.6, 4.1, 4.4, 4.5 and 6.4 of the textbook according to


the Course Schedule, but with an emphasis on more recent material


covered after the second test. If less common formulae are needed


on the exam, then those formulae will be provided on the exam.


There will be several questions, some with a few parts. Marks for


each question will be indicated. You have to show all your work,


and you should explain your solutions where appropriate.


Unofficial final grades for the course will hopefully be posted to


the course web page by Friday, June 28.


Please also note that I will be holding an additional office  hour for


last minute questions on Tuesday, June 18 from 16:00 to 17:00.

June 11:

I am making available solutions Test #2 questions. Please note that


the graded test papers will be ready to pick up on Tuesday, June 18.


Homework problems for Sections 2.4, 3.5 and 4.2:


Section 2.4: # 5; 6(a),(b); 7(a),(b),(c),(d),(f);


Section 3.5: # 4; 9; 10; 11;


Section 4.2: # 1; 4.

June 07:

I am making available  solutions  to Homework problems from


Sections 3.2 and 3.3.

June 06:

As it was announced in the class today, we will write Test #2 at


the first half of the class on Tuesday, June 11. On the test you will


be responsible for all the material that was covered in class from


Sections 2.1, 2.2, 2.5, 3.1, 3.2, 3.3, 3.4, 3.6, 4.1, 4.4 and 4.5


of the textbook.

June 05:

As it was promised in the class yesterday, I am making available


solutions  to Homework problems from Sections 2.2, 4.4 and 4.5, and


Part V of Professor Salisbury’s Lecture Notes.

June 02:

Please note that the student course evaluations are available on-line


at the URL link:  http://courseevaluations.yorku.ca  until Tuesday,


June 18, 2013. It is the time for you to be the judge. Please go


on-line and complete the course evaluation.

May 29:

Homework problems for Sections 3.2, 4.1 and 3.3:


Section 3.2: # 5; 8; 11; 13(a),(b),(c),(e); 14;


Section 4.1: # 3(e); 4(a),(b),(c); 9;


Section 3.3: # 2, 3, 5, 17, 20, 23.


I am making available  Part IV  of Professor Salisbury’s Lecture Notes.

May 28:

I am making available solutions to the questions of  white  and  green


versions of Test #1. Please note that the graded test papers will be


returned in the class on Thursday, May 30.

May 24:

Homework problems for Sections 2.1 and 2.2:


Section 2.1: # 2, 6, 7;


Section 2.2: # 6, 8, 9, 12.

May 20:

As it was announced in the class on Thursday, we will write Test #1


at the first half of the class on Thursday, May 23. On the test you will


be responsible for all the material that was covered in class from Sections


1.1, 1.3, 1.4, 1.5, 1.6 and Appendix 1 of the textbook. On the test you


will also be responsible for the material that we started covering on


Thursday’s class and that I am planning to finish on Tuesday’s class on:


Representing discrete and continuous distributions (Section 3.1, pages


140-141 and Section 4.1, pages 259-271);


Cumulative distribution functions (c.d.f.) and their relation with densities


and discrete distributions (Section 4.5);


Using c.d.f.-s to compute distributions of transformed random variables


(Section 4.5, pages 320-323).


Homework problems for Sections 3.1, 4.1, 4.4 and 4.5:


Section 3.1: # 9;


Section 4.1: # 2(a); 3(a),(b),(c),(d); 12(b);


Section 4.4: # 4; 10(b);


Section 4.5: # 2(a); 5; 6(a),(b),(c).

May 19:

I am making available solutions to Homework problems from


Sections 1.4, 1.5, 1.6 and  Part III  of Professor Salisbury’s


Lecture Notes.

May 16:

I am making available solutions to Homework problems from


Appendix 1 and Sections 1.1, 1.3.

May 12:

Please note that Tutorials for the course will be done in MathLab,


S525 Ross Building, which is open throughout the term:


Monday-Thursday from 11:00 to 13:00 and from 15:00 to 17:00.


I am making available  Part II  of Professor Salisbury’s Lecture Notes.

May 08:

As you asked in the class yesterday, I am making available  Part I  of


Professor Salisbury’s Lecture Notes.

May 07:

Welcome back!


To view and/or print PDF files you need to download the free Acrobat Reader  Description: C:\Users\raguimov\Desktop\getacro.gif


Homework problems for Chapter 1 and Appendix 1:


Section 1.1: # 2, 3, 7;


Section 1.2: #2, 3;


Section 1.3: # 4, 5, 6, 9, 10;


Appendix 1: # vii, viii, x, xi, xii, xiii;


Section 1.4: # 4, 5, 6, 7, 8, 12;


Section 1.6: # 4, 6, 7, 8;


Section 1.5: # 2, 3, 5 (a)-(d).


Course Information:



S1 2013





Lectures (day, time and venue):

T/R 18:0-21:00, CLH E



Dr. Iulduz Raguimov



S512 Ross






416-736-2100, EXT. 66092


Office Hours:

TR 16:00 – 17:00, also by appointment


Two Class Tests:



Final Examination:


Course Description: Introduction to the theory of probability as preparation for further study in both mathematical or applied probability and statistics. Topics include probability spaces, conditional probability, independence, random variables, distribution functions, expectations, Chebyshev's inequality, common distributions, moment-generating functions, laws of large numbers and limit theorems.

This course provides an introduction to the theory of probability. It covers the mathematics used to calculate probabilities and expectations, and discusses how random variables can be used to pose and answer interesting problems arising in nature. It is required for most programs in Mathematics and Statistics, or in Computer Science. Subsequent courses that use the material covered include mathematical statistics, operations research, mathematical finance, stochastic processes as well as advanced courses in probability.

For a more detailed list of topics with references to the textbook, please see Course Schedule.


Probability, First Edition

by Jim Pitman


Springer-Verlag, 1993. ISBN 0-387-97974-3

Course Prerequisites:

One of SC/MATH 1010 3.00, SC/MATH 1014 3.00 or SC/MATH 1310 3.00.

Degree Credit Exclusions:


Important Dates:

May 07: Classes commence

May 10: Last date to enrol in the course without my permission

May 17: Last date to enrol in the course with my permission

May 31: Last date to drop the course without receiving a final grade

June 14: Classes end

June 19-21: Final Examination, TBA.

Course Schedule:
(subject to any changes announced in class)




May 6-10

1.1-1.4, Appendix 1

Lectures begin Tuesday, May 07.

May 13-17

1.6, 1.5, 3.1, 4.1, 4.5

May 20-24

2.1-2.2, 3.2, 4.1

Test #1 will take place on Thursday, May 23.

May 27- 31

3.3, 3.4, 2.5, 3.6

June 3-9

3.1, 3.3, 2.4, 3.5

June 10-14

3.1, 6.4, Review

Test #2 will take place on Tuesday, June 11.
Classes end on Thursday, June 13.

June 19-21

Final Examination


Note 1: Not all topics of the sections above will be covered and it is not necessary that we will cover the topics in the same order as the textbook presents them.
Note 2: It is recommended to read the relevant sections of the textbook before every lecture.


Throughout the term, homework problems will be posted to the Announcements section of the course web page. In order to develop your understanding of the course material you must do all assigned problems. These will not be collected for grading and hence will not directly affect your grade. However, it is extremely important that you complete all assigned exercises. Do not memorize them. Rather, learn how to solve problems like them. Learning Mathematics is not a spectacular sport, it is a participatory event. There is nothing like a bit of computation to strengthen understanding in mathematics! Use the Solutions Manual only after you have tried the problem. Solutions to typical homework problems will be posted to the course web page. Successful students must keep up with homework and seek help for points they do not understand as soon as possible. Do not fall behind! It is recommended to read the relevant sections of the textbook before every class. Next to the classes, working out the answers to the problems is the most important preparation for the tests and exam that will contain for the most part but not exclusively, questions very similar to those from the textbook. It is quite practical to work on your own or together in small groups. Each student should do at least two hours of independent study for every lecture hour. The amount you learn in this course and the grade you receive will be proportional to the amount of time you spend working on problems.


Exams Information:

Lecture/Test Rules:

Please turn off all cell phones, iphones, ipods, ipads and pagers before entering the lecture hall. For the tests and exam cell phones, iphones, ipods, ipads, calculators, digital dictionaries, palms, pagers or any other internet connected devices are NOT allowed. All such devices as well as all books, papers, knapsacks and briefcases must be left at the front of the lecture hall. Anyone caught with electronic devices will be charged with Academic Dishonesty (see the next page). The only items you may have at your seat are pens, pencils, student ID and purses. You are responsible for all material covered in lectures.
Note: Photo identification and signing-in are required at all tests and exam.

Final Grade:

The official grades at York University are LETTER grades. Qualitative descriptions of these grades can be found in the York Calendar at this link.Your test marks will be on a numerical scale because these have to be weighted and averaged in various ways, but THERE IS NO AUTOMATIC PREDETERMINED CORRELATIONS BETWEEN NUMERICAL GRADES AND LETTER GRADES in this course. In particular, the "numerical" grades you receive are NOT to be interpreted as percentages; they are merely 'raw scores'. Once the tests are returned in class, the distribution of 'raw scores' will be announced along with their approximate conversion to letter grades. The median letter grade for the course will likely fall between C and C+.
The composition of the final grade is as follows:
Two class tests (75 minutes each, written tests held in lecture periods): 25%+20% of the overall grade (Tentative dates for the tests: Thursdays, May 23 and Tuesday, June 11, 2013).
Final examination
(3-hour exam scheduled by the Registar's Office): 55% of the overall grade, will take place during the examination period between June 19 and 21, 2013.
Students have five days from the date of the return of test papers to appeal their marks. Some test papers (randomly selected) are photocopied before they are handed back, so we can detect subsequent alterations.

Make-up Policy:

No permission will be given to a student to write the tests in advance of their scheduled dates. No make-ups will be done for the tests. A missed test will be counted as zero, except under extreme circumstances in which case the corresponding percentage of the overall grade will be "forwarded" to the final exam. If you miss a test for medical reasons, you must turn in within one week following the test date the Attending Physician's Statement form provided  here  after getting it filled in by your doctor. No other type of medical note will be accepted. However, missing tests is extremely dangerous and not recommended. As experience has shown, students who miss class tests because of some 'mysterious illnesses' will usually average 30% on the final exam. A student who misses the final examination will be allowed to write a make-up exam only if both of the following conditions are met:
1) the student notifies me (raguimov@mathstat.yorku.ca) or the Department of Mathematics and Statistics (Undergraduate Office, N502/503 Ross Building, 416-736-2100 416-736-2100, Ext. 55902 or 33969) in advance that the exam will be missed,
2) the student submits within one week following the exam date the Attending Physician's Statement form provided  here  after getting it filled in by his/her doctor.
Students who miss the final examination and do not meet both conditions will receive a grade of F. It is student's responsibility to fill out and submit the Deferred Standing Agreement Form.
Note: Do not make vacation/job plan until the final exam date is known: having a plane ticket for Banff or Hawaii on June 15 is NOT a legitimate excuse for absence from a final examination on June 21.

Religious Observance:

York University is committed to respecting the religious beliefs and practices of all members of the community and making accommodations for observances of special significance to adherents. If any of the dates specified in the course schedule for in the tests pose such a conflict, students should contact me (raguimov@mathstat.yorku.ca) within the first two weeks of classes. Please note that if the final exam date poses a conflict, students must complete the Examination Accommodation Form, which can be obtained from the Registrar’s Office.

Academic Honesty:

Students are responsible for familiarizing themselves with University Policies and Regulations. Conduct that violates the ethical or legal standards of the university community or of one’s programme or specialization may result in serious consequences. Refer to the Senate Policy on Academic Honesty.


Individual questions can be discussed by e-mail, or in person after class, or during office hours. Please send all e-mail notes as plain text within the body of the message. Do not send attachments or HTML-formatted mail. Also, if the name of your account is an alias, I will not know who the mail is from unless you sign it; it also risks being accidentally discarded as junk mail. The course web page will be up-dated regularly to include important announcements made in class, such as the material to be covered on the exams and quizzes. Email notes requesting such information contained on the web page will be answered the last.

Links and Other Resources:

1- York Undergraduate Mathematics Program
2- York University Library
3- Online Forum
4- How To Write Proofs
5- Local time in Toronto

Questions and comments regarding this Web page please send to raguimov@mathstat.yorku.ca

© 2003-2013, All Rights Reserved, York University & Iouldouz S.Raguimov

Last updated June 27, 2013