Mathematics 362K Spring 2014 (Unique ID 56955)

Answers to the final

Instructor: Dave Rusin (

Office hrs: TTh 2-3, W 12-3, and by appointment, in RLM 9.140 . (I am usually in my office during ordinary business hours but if you want to be sure I'm available, let me know in advance.)

Text: Sheldon Ross, A First Course in Probabilility, 9th edition

Class meets Tuesdays and Thurdays 12:30--2:00pm in ECJ 1.204

Course webpage:

Course description:

An introductory course in the mathematical theory of probability, fundamental to further work in probability and statistics, includes basic probability properties, conditional probability and independence, various discrete and continuous random variables, expectation and variance, central limit theorem, and joint probability distributions.


Completion of Calculus M408D, M408L, or M408S with a grade of at least C-.


I will assign homework approximately once per week; it will be due one week later unless otherwise indicated. I will drop two homework scores and average the rest to give you a homework score (which I will scale to a 100-point scale). If you miss a homework for any reason that will simply become one of your two dropped homeworks -- I don't accept late homeworks. I will grade as rapidly as I can but there are a lot of you... Your homework answers (and test answers) must show your work and explain your logic. You're not in calculus any more: get used to expressing your thoughts in sentences and paragraphs!

I promised I would keep a list of the assigned problems online: here you go!


There will be in-class exams on Thursday, February 27 and Thursday, April 3. Our final exam will be Thursday, May 8, 2:00-5:00pm. The final exam will be comprehensive, but there will be more weight on material from the end of the term. You will get a numerical score on each exam, but not a letter grade (see next section).

Semester grade:

I will weight the components of the course as follows:
 15% homework
 25% exam 1
 25% exam 2
 35% final

I will try my best to let you know as we go along how well you're doing in the class, but please note that I am NOT promising any particular conversion of numerical scores to letter grades. In my experience, students underestimate the depth of understanding that I expect of them, and as a result the numerical scores on the exams tend to be low -- I will likely be pointing out to you lots of ways that you could improve your answers. But I do not intend to penalize you guys for having chosen a demanding teacher -- your letter grades will be similar to those of the rest of the UT math department: roughly speaking if you are above the mean score (and that's typically more than half the class) you are an "A" or "B" student; most of the remaining students are operating at "C" level. I will always try to tell you when I return an exam which students I think are in trouble (i.e. performing at a "D" or "F" level).

General Policies


it is in general not possible to make up missing quizzes or homework assignments after the due date. If you believe you will have to miss a graded event, please notify me in advance; I will try to arrange for you to complete the work early.

Students with disabilities:

The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

Religious holidays:

If you are unable to participate in a required class activity (such as an exam) because it conflicts with your religious traditions, please notify me IN ADVANCE and I will make accommodations for you. (University policy requires that a student must notify each instructor at least fourteen days in advance if they are going to miss required course work due to a religious observation.) Typically I will ask you to complete the required work before the religious observance begins.

Academic Integrity:

Please read the message about Academic Integrity from the Dean of Students Office. I very much prefer to treat you as professionals whose honesty is beyond question; but if my trust is violated I will follow the procedures available to me to see that dishonesty is exposed and punished.

Campus safety:

Please familiarize yourself with the Emergency Preparedness instructions provided by the university's Campus Safety and Security office. In the event of severe weather or a security threat, we will immediately suspend class and follow the instructions given. You may wish to sign up with the campus alert programs.

Drop dates:

Jan 29 is the last day to drop the course for a possible refund; March 31 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class except for urgent and substantiated, nonacademic reasons. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page, I will happily advise you about whether I think you should drop the course: typically students with A's, B's, and C's should complete the semester, while students who are getting D's and F's despite trying all effective strategies should withdraw. I would love to turn in a semester grade sheet with no D's or F's!

Note: No student may enroll in any course in the College of Natural Sciences more than twice, even if the course is needed to meet degree requirements, without first obtaining the written consent of his or her major adviser and of the department that offers the course; students in colleges other than the College of Natural Sciences need only departmental approval. A symbol of Q or W counts as an enrollment unless it has been approved by the dean's office for nonacademic reasons.


You'll need a calculator that can handle factorials and exponentials, nothing more. We don't make use of sophisticated software in this class, but if you find this interesting, you are welcome to use the department's computer facilities. Our 40-seat undergrad computer lab in RLM 7.122, is open to all students enrolled in Math courses. Students can sign up for an individual account themselves in the computer lab using their UT EID. We have most of the mainstream commercial math software: Mathematica, Maple, Matlab, etc., and an asortment of open source programs. If you come to my office you will see me use some of this software to help illustrate concepts. Please see me if you would like more information.

Student Conduct:

Please come to class on time. If you will be late or need to leave early for some legitimate reason, please sit near the exit. Coming and going during class is distracting to your fellow students, and they do not like it; we know this because they complain about it. Please do not talk or otherwise disturb students in the class who are trying to learn.

All computers, cell phones and other hand-held devices must be put away out of sight during class and during exams.

Do not cheat. If you are caught cheating, you will be penalized as harshly as possible under the rules of UT.


You are expected to attend daily and follow along with the discussions in class; we will vary the pace as needed to ensure student understanding. But my goal is to cover the following sections according to the schedule shown, so please read each section BEFORE class:
Jan 14-16: 1.1-1.4, 2.2
Jan 21-23: 2.3-2.5
Jan 28-30: 2.7, 3.1-3.3
Feb 4-6: 3.3-3.4, 4.1-4.2
Feb 11-13: 4.3-4.5
Feb 18-20: 4.6-4.8
Feb 25-27: review and exam
Mar 4-6: 5.1-5.4
Mar 11-13: Spring break
Mar 18-20: 5.4-5.7
Mar 25-27: 6.1-6.5
Apr 1-3: review and exam
Apr 8-10: 7.1-7.5
Apr 15-17: 7.7-7.8, 8.1-8.2
Apr 22-24: 8.3-8.4
Apr 29-May 1: Review
Thurs May 8: Final exam in our regular classroom, 2-5pm