Math 362, Introduction to Probability, Fall 2015

Information TypeData
Meeting TimeMWF, 9:00—9:50
Meeting Room CHVEZ 105
InstructorProfessor Marek Rychlik
OfficeMathematics 605
Homepage (Mirror)

Office Hours

PersonnelDay(s) of the WeekHourRoomComment
Marek RychlikM10:30pm—11:30pmMathematics 605Regular Office Hours in my office
Marek RychlikM2:30pm—3:30pmMathematics 605Regular Office Hours in my office
Marek RychlikW11:00—12:00Mathematics 220Math Upper-Division Tutoring

Required Texts

Introduction to Probability and Its Applications, Third Edition, Richard L. Sheaffer, Brooks/Cole Cengage Learning, required.

Required Examinations And Other Grade Components

  • Three 1-hour Midterms, worth 15% of the course grade each
  • A 2-hour Final Exam worth 30%.
  • Weekly Quizzes worth 12.5% (see below for details).
  • Written homework with use of R, worth 12.5% (see below for details).
  • Daily attendance and participation Quizzes worth 5% of extra credit (see below for details).


  1. Math 223.
  2. Access to a computer running R software.
  3. A compatible Radio-Frequency Responder (clicker).


Homework is assigned throughout the semester. Two types of homework will be assigned:

  1. Homework which consists in solving selected odd-numbered problems from the book; this homework is not collected or graded, but is used as a basis for quizzes and exams (see below).
  2. Homework which involves working with a computer and software system R; this homework is collected and graded.

Homework, class attendance and class participation are evaluated as follows.

  1. There will a weekly 15-minute announced quiz directly based on the homework. The quizzes will be administered every Wednesday, except when a midterm takes place. The quizzes will be conducted using radio-frequency responders (otherwise known as "clickers"). Quizzes are worth 12.5% of the grade.
  2. There will be an attendance quiz on Monday and Friday, typically lasting 1-2 minutes and consisting of one question related to the material. Attendance quizzes are worth 5% of ***EXTRA CREDIT***. The regular (Wednesday) quiz counts also as an attendance quiz.
  3. There will be 8 graded written homework assignments involving work with the R software environment. These R assignments are worth 12.5% of the grade.

Extra Credit Assignments

Numerical Experiments

There will be a number of extra-credit assignments involving Monte-Carlo experiments with R. Credit will vary according to the difficulty and time involved.

Individualized assignments involving applications

These assignments will be proposed by the student and approved by the instructor. Credit will vary depending on the difficulty and time involved.

Overall Course Objectives and Expected Learning Outcome

  1. Learn in detail the fundamental concepts of probability theory: sample spaces and random variables.
  2. Learn how to apply probability theory to numerous problems of science, engineering and "real life".
  3. Gain a better understanding of the concepts of probability through computer exercises performed in the R language, and hands-on activities.

Course Outline

WeekDatesTopicsSections Covered
1Aug 24—Aug 28 Probability in the World Around Us. Randomness with known and unknown structure. Introduction to R. 1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.2
2Aug 31—Sep 4 Sample Spaces and Events. 2.3
3Sep 7Labor Day - no class.
3Sep 9—Sep 11 More on sets, sample spaces, events. Inclusion-Exclusion Principle for 2 sets and 3 sets (Example 2.2). 2.2, 2.3
4Sep 14—Sep 18 Definition of Probability. Counting Rules Used in Probability. 2.4, 2.5
5Sep 21Counting rules. Multi-stage processes. Two-way tables. Probability trees. Review for Midterm 1.2.4, 2.5
5Sep 23 TAKE-HOME MIDTERM 1 POSTED. Counting Rules. Permutations, Combinations. Distinct vs. identical items. 2.4, 2.5
5Sep 25 Counting Rules used in Probability. Review of Take-Home Midterm 1 topics. Assignment R2.
6Oct 6 NOTE: This syllabus item is added purely to describe R Assignment 3. The topics in this assignment cover: counting rules, conditional probability, Bayes Formula, computing contingency tables with R, computing multinomial coefficients. First encounter of the multi-nomial distribution. 2.4, 3.1, 3.2, 3.3
6Sep 28—Oct 3 Conditional Probability. Independence. Theorem on Total Probability and Bayes Rule. 3.1, 3.2, 3.3
7Oct 5—Oct 9 Theorem on Total Probability and Bayes Rule. 3.3
8Oct 12—Oct 16 Random Variables and Their Probability Distributions. 4.1
9Oct 19Review for Midterm 2.
9Oct 21Midterm 2.
9Oct 23 Random Variables and Their Probability Distributions. The Bernoulli Distribution. The Binomial Distribution. 4.1, 4.2, 4.3
10Oct 26—Oct 30 Independence of Random Variables. Distribution of a sum of independent random variables. Convolution of probability functions. Expected Value of Discrete Random Variables. Variance. 4.4, 4.5, 4.6
11Nov 2—Nov 6 Tchebysheff's Inequality. The Geometric Distribution. The Negative Binomial Distribution. The Poisson Distribution. The Hypergeometric Distribution. 4.7, 4.8, 4.9, 4.10
12Nov 9—Nov 13 The Moment-Generating Function. The Probabilty-Generating Function.
12Nov 11 Veteran's Day - no class.
12  The Moment-Generating Function. The Probabilty-Generating Function. 4.11, 4.12
13Nov 23—Nov 27 Continuous random Variables and Their Probability Distributions. 5.1, 5.2
14Nov 30Review for Midterm 3. Expected Values of Continuous Random Variables. The Uniform Distribution. The Exponential Distribution. 5.3, 5.4
14Dec 2Midterm 3.
14Dec 4 The Gamma Distribution. The Normal Distribution. 5.5, 5.6
15Dec 7—Dec 9 Expectation of Discontinuous functions and Mixed Probability Distributions. Review before the Final Exam.
Finals WeekDec 15 (Tuesday)Final Exam, 10:30 am - 12:30 pm (regular room).

Course Policies

Attendance Policy

Students are expected to attend every scheduled class and to be familiar with the University Class Attendance policy as it appears in the General Catalog. It is the student's responsibility to keep informed of any announcements, syllabus adjustments or policy changes made during scheduled classes.

Expected Classroom Behavior

Students are expected to behave in accordance with the Student Code of Conduct and the Code of Academic Integrity. The guiding principle of academic integrity is that a student's submitted work must be the student's own. University policies can be found at

Threatening Behavior

See No prohibited behavior will be tolerated.

Administrative Drop

Students who miss the first two class meetings will be administratively dropped unless they have made other arrangements with the instructor.

Missed Exams

Students are expected to be present for all exams. If a verifiable emergency arises which prevents you from taking an in-class exam at the regularly scheduled time, the instructor must be notified as soon as possible, and in any case, prior to the next regularly scheduled class. Make-up exams and quizzes will be administered only at the discretion of the instructor and only under extreme circumstances. If a student is allowed to make up a missed exam, (s)he must take it at a mutually arranged time. No further opportunities will be extended. Failure to contact your instructor as stated above or inability to produce sufficient evidence of a real emergency will result in a grade of zero on the exam. Other remedies, such as adjusting credit for other exams, may be considered.

Accessibility and Accommodations

Disabled students must register with Disability Resources and be identified to the course instructor through the University's online process in order to use reasonable accommodations.

It is the University's goal that learning experiences be as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, please let me know immediately so that we can discuss options. You are also welcome to contact Disability Resources 520-621-3268 to establish reasonable accommodations.

Please be aware that the accessible table and chairs in this room should remain available for students who find that standard classroom seating is not usable.

Policy on the grade of "I" (incomplete)

The grade of "I" will be awarded if all of the following conditions are met:

  • The student has completed all but a small portion of the required work.
  • The student has scored at least 50% on the work completed.
  • The student has a valid reason for not completing the course on time.
  • The student agrees to make up the material in a short period of time.
  • The student asks for the incomplete before grades are due, 48 hours after the final exam.


Changes to the Syllabus

The information contained in the course syllabus, other than the grade and absence policies, is subject to change with reasonable advance notice, as deemed appropriate by the instructor.