STA104/MTH135: Probability

Lectures:Tue Thu 10:05-11:20am Soc Sci 139
Prof:Robert L. Wolpert TAs: Jared Murray, Mike Seo
Office: Old Chem 211c, 684-3275 Old Chem 211a, 684-8821
OH:Wed 1:30-2:30pm Find steel blue names on SECC Schedule
Tue Thu 11:20-11:30am (after class, in classroom)

Course: Syllabus Exam Formula Sheet
Computing: R MatLab


This is a basic calculus-based first course in the theory and application of probability. It develops quantitative methods for solving problems that involve uncertainty, and provides a foundation for the further study of statistics or random processes. Many probability calculations are based on summing infinite series or on evaluating integrals, often in more than one dimension, so multivariate calculus at the level of MTH103 is a prerequesite (or at least corequesite) for this course. If you are unsure about your calculus preparation, try this diagnostic quiz.

The course text is Jim Pitman, Probability (1st edn 7th printing). All class materials are distributed on-line via the web; for example, you will be able to view homework assignments (and sometimes class notes) on the Syllabus.

Homework Assignments

The only way to be sure you're learning the course material is to solve problems (or, as Sophocles put it, One must learn by doing the thing; for though you think you know it, you have no certainty until you try.) Eleven weekly problem sets are assigned through the on-line syllabus. Homeworks are collected at class each Thursday, and are (usually) returned the following Tuesday class after which solutions will be posted on the web. Late homeworks are accepted with a penalty of about 10% per day, up until the solutions are posted. Lateness penalties are waived for students with excused absences, and for all students the lowest homework score will be dropped.

You may work with other students on the homework problems, but your final answers should be written up independently: copying homework solutions is not allowed. You are encouraged to ask the professor and the TA for help on your homework (in person or by e-mail), after you have tried to solve the problems on your own. Questions about homework scores should first be addressed to the TA.

For full credit on homework assignments and exams, numerical answers should be given either as fractions in lowest terms (2/3, not 17/51), or as decimals to four significant places (0.6666 or 0.6667, not 0.6 or 0.7)— not as expressions still in need of evaluation (like elog 2 -0.25 log 81), even if they're correct (and even if the ‘Brief Solutions’ in the text give something else).

HELP is available! The TA and I both have office-hours (see above); in addition, Duke Statistics maintains an open Help Session every Sun-Thu in the Statistical Education and Consulting Center, located in room 211b Old Chem, where a statistics graduate student will be happy to help you (detailed times and staffing are listed on the SECC website). There may also be grad students from other departments, helping students in the introductory statistics courses--- be sure to find a Duke Statistical Science grad student (they're listed in steel blue on the TA Schedule.). Our own TA Jared will be there each Wed 6-7:30pm and Thu 4-5:30pm, for example).

Sometimes it's helpful to see another authors' description of the same concepts. Here's a free book that's pretty good.


Some homework assignments will have a computing component. You may use whaterver computing environment you prefer; good choices include MatLab, R, S-Plus, C, Mathematica, or Maple (all of these will become tools you can use in later work, making them preferable to spreadsheets like Excel, old-fashioned statistics environments like SAS or SPSS, introductory languages like BASIC or Pascal). If you are undecided I would recommend Matlab, for which you can get help from your instructors and can find a free primer or guide or other help on the web, or the free open-source statistical software environment R (or its commercial work-alike, S-Plus), for which your instructors can also help. The R software is open-source and free, and works well under windows, mac-OS, and linux; Matlab is expensive, but is commonly used in engineering courses and is installed in all the OIT computer labs.


In each week's lectures I will try to help clear up topics that many find difficult, and will try to illustrate tough (or fun) ideas with interesting examples. I can not cover every important topic in class, however, there just isn't enough time. The syllabus lists reading assignments each week (it's just the textbook chapter preceeding the next week's homework problems); you are responsible for learning the material from any combination of the text, problems, and lectures. Please ask questions in class or office-hours or by e-mail if you are struggling (or just curious) about topics from that week's readings.


In-class Midterm and Final examinations are closed-book and closed-notes with a formula sheet permitted (one-sided, 8½"×11" for each midterm, and two-sided, 8½"×11" for the final). You should bring to each exam a calculator capable of computing exponentials, powers, and factorials. Any questions regarding exam grades should be taken up with the professor. Tests from recent MTH135/STA104 offerings are available to help you know what to expect and to help you prepare for this year's tests.
Fall 2005: 1st Midterm 2nd Midterm Final Exam
Fall 2008: 1st Midterm 2nd Midterm Final Exam
These old exams and several other course materials (e.g., the diagnostic
quiz) are offered in Adobe PDF format. All computers in Duke OIT labs are configured properly to display and print PDF documents; if your home computer is not, click here: Download Adobe PDF Reader to get the Adobe Reader plug-in for your browser. Solutions will not be made available for these old tests, but the TA or Prof will be happy to check your solution after you make a good-faith effort to solve old test problems.


Course grades are based on two in-class Midterm Exams (20% each), ten weekly Homework assignments (20% total), and a cumulative Final Exam (the rest, 40%). If it seems helpful I may give occasional short in-class quizzes, which will count no more than 5% of the grade (reducing the weight of the final exam). Missed homeworks receive zero scores and late homeworks are penalized, but the lowest homework score is dropped. Histograms and summary statistics of midterm and final exam grades will be added to the syllabus web page. Each student's current average and course grade are available from the instructor at any time.

Academic Integrity

Cheating on exams, plagiarism on homeworks and projects, lying about an illness or absence and other forms of academic dishonesty are a breach of trust with classmates and faculty, and will not be tolerated. They also violate Duke's Community Standard and will be referred to the Undergraduate Judicial Board (UJB).

Excused Absence

Students who miss tests or assignments due to a scheduled varsity athletic trip or religious holiday should submit an on-line NOVAP or RHoliday form, respectively, at least a week ahead of time and meet with me to arrange to make up the work (often before the scheduled event).

Those with a personal emergency or bereavement should seek a Dean's Excuse; check with your academic dean for details, and see me as soon as possible after your return to schedule make-up work. Duke does not issue Dean's Excuses for short-term incapicating illness; if you are too ill to complete an assignment or attend an examination, inform me as soon as possible using the on-line IllnessForm (there seems to be a separate form for grad. & prof. students), and see me to make arrangements to make up the missed work.

No excuse is needed simply for missing class, only for missed assignments and examinations. Note that the Community Standard sanctions apply for abuse of this procedure.