F18 STA230/MTH230/MTH730: Probability

Lectures:Mon Wed 10:05-11:20 116 Old Chem
Prof:Robert L. Wolpert TA: Ed Tam
E-mail: rlw@duke.edu edric.tam@duke.edu
Office: 211c Old Chem, 919-684-3275 203 Old Chem
OH:Mon 3:30-5:00pm Tue 12:00n-2:00pm
Mon Wed 11:20-11:30am (after class, in classroom)

Course: Syllabus Exam Formula Sheet Diagnostic Quiz
Computing: R MatLab Python


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 multivariable calculus at the level of MTH112L is a prerequisite for this course. If you are unsure about your calculus preparation, try this diagnostic quiz.

The course text is Jim Pitman, Probability. 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 and exam scores will be reported through Sakai.

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 the start of class each Wednesday (so I can answer questions about them in class), and are (usually) returned the following Monday class after which solutions will be made available. They may also be submitted electronically to Sakai's "Drop Box," with a time stamp before the start of class. 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 (see Academic Integrity section below). You are encouraged to ask the professor and the TAs 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 TAs.

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 or Σn≥1(2/5)n) ), even if they're correct (and even if the ‘Brief Solutions’ in the text give something else).

Sometimes it's helpful to see another author's description of the same concepts. Here's a free book that's pretty good, if you'd like to see another presentation of the material.


Some homework assignments will have a computing component. You may use whatever computing environment you prefer; good choices include R, Matlab, Python, 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 Stata or SPSS, pedagogic intro statistics environments like JMP or Minitab, or introductory computing languages like BASIC or Pascal. If you are undecided I would recommend the RStudio environment for the free open-source statistical software environment R. Especially if you already have experience with it, another good choice is the engineering staple Matlab, for which you can get help from your instructors and can find a free primer or tutorial on the web. Yet another good choice is the general computing environment Python, for which your instructors can also help. Both R and Python are open-source and free, and work well under windows, OS-X, and linux. Matlab is proprietary and expensive, but is commonly used in engineering courses and is available in all the OIT computer labs and VMs.


In each week's lectures I will try to help clear up topics that many students 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 (the green or blue textbook chapter number on the left of each row); you are responsible for learning the material from any combination of the text, problems, and lectures. Sketchy lecture notes are available for most weeks' lectures (click on the chapter number), but lectures are dynamic and often include examples or topics beyond those notes, and may omit topics covered in the text that nevertheless appear on homeworks or exams. Please ask questions in class or office-hours or by e-mail if you are struggling (or just curious) about topics from the readings or lectures.


In-class Midterm and Final examinations are closed-book and closed-notes, but you may bring and use a single 8½"×11" sheet of your own notes. You should bring to each exam a calculator capable of computing exponentials, powers, and factorials. No phones, tablet devices, or laptops may be used--- all such devices, notes and other materials must be on the floor. Tests from a couple of MTH230/STA230 offerings a few years ago are available to help you know what to expect and to help you prepare for this year's tests:
Fall 2010: 1st Midterm 2nd Midterm Final Exam
Fall 2013: 1st Midterm 2nd Midterm Final Exam
Solutions will not be made available for these old tests (feel free to ask me why), but the TAs or Prof will be happy to check your solutions 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 homework). 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 professor at any time. Historically the median grade has been close to the A-/B+ border.

Academic Integrity

Cheating on exams, plagiarism on homeworks and projects, copying homework, 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 Dean of Students' Office of Student Conduct as described here: Academic Integrity Council. Additionally, there may be penalties to your final course grade.

Excused Absence

Class attendance is completely optional— no excuse is needed simply for missing class, only for missed assignments and examinations.

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 inform me and your academic dean of your predicament, and see me as soon as possible after your return to schedule make-up work. If you are too ill to complete an assignment or attend an examination, inform me as soon as possible using the on-line Short Term Illness Form and see me to make arrangements to make up the missed work. Note that the Community Standard sanctions apply for abuse of this procedure.