MATH 362K: Probability I

General Information

      Unique ID: 54570 --- Spring 2015

      Instructor: Dave Rusin ( 
      Office hrs: Tues & Thurs 2pm-4pm, Wed 3pm-4pm, 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 T,Th in NOA 1.102, 11:00-12:30 pm. Plan now so that you 
      will have time to eat lunch at some other time than in class!

      Registration in this section is closed; I can't put anyone else
      into the course. If you think you will probably drop the course,
      please do so promptly and allow another student to take your place.

      Your final exam is Friday, May 15, 2:00-5:00 pm. It may not be
      in the regular classroom; I will announce the location when I know it.
      There is no provision for taking the final exam earlier or later.

Course webpage: It is unlikely that I will post any important material to Blackboard or Canvas; for any additional information I want to give you outside of class you should come to this webpage.


Here are the current homework assignments By popular demand I place here a previous
  • final and
  • answer key.

    Catalogue Description

    An introduction to 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.


    Mathematics 408D, 408L, or 408S with a grade of at least C-. Please note that if you had a C- in one of those courses, you have the weakest background in the class and so you should be working hardest and getting the most help and feedback from me.

    Mathematics 362K and Statistics and Scientific Computation 321 may not both be counted.

    Graded material

    Your semester grade will be based on a number of components. This structure is designed to encourage you to stay actively involved in the course all the way through the semester. Any adjustments to the schedules or policies will be announced multiple times in lecture and via email and on the course website shown above.

    Homeworks: 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!

    Exams: There will be 2 mid-term exams, to be held during the usual class period, and a comprehensive final exam. Each midterm is worth 100 points and the final is worth 200 points. I expect the dates of the midterms to be Thursday Feb 19 and Thursday Apr 9. Please mark on your calendars now the time and date of the exams. (I don't know yet what room the final exam will be held in.) Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams. The exams will be a mix of multiple-choice and free-response questions; the ratio will change as the semester progresses.

    Attendance: I will be at class every day and expect you to be, too, until the last day of our class (May 7). We will use the class time to work problems together and I *WILL* call you to come forward and explain things to the class. In particular: I'll notice if you're not there...

    Letter Grades

    Your semester grade is based only on the number of points accumulated from the above mix of 500 possible points. I will use this conversion table:
    Point total Semester grade
    450-500 A
    430-449 A-
    420-429 B+
    400-419 B
    380-399 B-
    370-379 C+
    350-369 C
    330-349 C-
    320-329 D+
    300-319 D
    280-299 D-
    0-279 F
    If for some reason there is a deviation from this scale it will be applied uniformly to the whole class, and it will be announced in class. I promise that if anything, I will only make the scale more generous! WARNING While the letter grade distributions in my classes tend to look like those of other instructors, students often report that my tests tend to be difficult and long, and so the numerical scores are not high. Here is what the mean scores were in a recent semester: (Standard deviations shown in parentheses.)

    You will notice that this mean score roughly separates the A's and B's from the C's, D's, and F's above; after all A and B are supposed to mean "above average", right? (Mean is not the same as median; most of the students last semester got A's and B's; only 11% of the letter grades were D's and F's.)

    No letter grades will be assigned to the midterms or homeworks, but you should keep track of where you stand: I will advise you of the class averages and you can use this data from other semesters as a rough guideline.


    Classroom activity: Our meeting times together are very short so we must make the most of them. Come to class daily and ask questions; this is greatly facilitated by reading ahead each day and doing the homework problems as they are assigned. Please silence your cell phones. I will always assume that any conversations I hear are about the course material so I may ask you to speak up.

    Make-ups: It is in general not possible to make up missing 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. 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.

    Counseling: Students often encounter non-academic difficulties during the semester, including stresses from family, health issues, and lifestyle choices. I am not trained to help you with these but do encourage you to take advantage of the Counselling and Mental Health Center, Student Services Bldg (SSB), 5th Floor, open M-F 8am-5pm. (512 471 3515, or

    Add dates: If you enroll within the first four class days of the semester, and have missed any graded material, I will adjust the weighting of your graded sections accordingly so that you are not penalized. No such accommodation is made for students who enroll on the 5th day or later. (Such students must enroll through the MPAA advising center in RLM, and ordinarily I do not admit students who ask to enroll then if they have missed any graded activities).

    Drop dates: Jan 23 is the last day to drop without approval of the department chair; Feb 4 is the last day to drop the course for a possible refund; Apr 6 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,

    Computers: 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.


    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 20,22: 1.1-1.4, 2.2
    Jan 27,29: 2.3-2.5
    Feb 3,5: 2.7, 3.1-3.3
    Feb 10,12: 3.3-3.4, 4.1-4.2
    Feb 17,19: 4.3 and exam
    Feb 24,26: 4.4-4.6
    Mar 3,5: 4.7-4.8
    Mar 10,12: 5.1-5.4
    Mar 17,19: Spring break
    Mar 24,26: 5.4-5.7
    Mar 31, Apr 2: 6.1-6.5
    Apr 7,9: review and exam
    Apr 14,16: 7.1-7.5
    Apr 21,23: 7.7-7.8, 8.1-8.2
    Apr 28,30: 8.3-8.4
    May 5,7: Review


    You may have spent most of your mathematical life working on problems by yourself. This is a good thing; you become self-reliant. However, I strongly encourage you to work with one or two other students in this class on a regular basis. Challenge each other to solve the problems, to explain the concepts, and to ask each other for help. This is the way mathematics is done in the real world, and practicing this now can help you this semester and beyond.

    Since you are adults, I leave it to you to monitor your level of understanding on your own, and to seek help when you need it. But please allow me to share my experience. Every student who starts this class has met the pre-requisites and has the expectation that he or she will succeed. Nonetheless, every semester, about one-fourth of this group of bright, hard-working students ends up with a D or F, or withdraws. No one likes this outcome. Please be attentive to your progress on homeworks and midterms. If you find you are always asking other people for help while studying; if you find that it takes you hours and hours to complete every homework set; if you score less than half the possible points on a midterm exam: in these cases, you CAN succeed, but ONLY if you change your patterns immediately. Optimism is a wonderful thing but it alone cannot bring the results you may want. Please see me early in the semester if you think you may have trouble during this course. I can try to help you with the material, or with your study habits, or else advise you to withdraw. Let's make this the first-ever 100% successful Math 362K class!

    One more suggestion: have fun this semester! Some of us think math is so cool that we end up doing it for a living. I will try to convey to you some of what's kewl, and invite you to consider majoring (or minoring) in math, joining the math club, or simply taking more math classes. I am always happy to talk in my office about mathematics topics beyond what we discuss in class.