Description of Course Goals and CurriculumORF 245 Fundamentals of Statistics covers a mathematical approach to statistics and probability. The course is the introductory course for the Operations Research and Financial Engineering department, but the probability and statistics learned in the class are applicable to scientists and engineers more broadly. The course begins with a short study of probability, but most of the semester is concerned with statistics. The topics covered are: probability, random variables (both discrete and continuous), point estimation, confidence intervals, hypothesis testing, classification, and regression. Many of the topics covered in the course require familiarity with calculus. Calculus concepts used most commonly are single and multi-variable derivation and integration. In addition to normal problem sets, the course also uses MATLAB to apply the course’s topics to real datasets and simulations. The first programming assignment as well as precept cover the basics of MATLAB needed for the course, so no prior MATLAB experience is expected. A general familiarity with basic programming constructs (e.g. loops and conditional statements) would be helpful but is also not necessary as the programming assignments focus on statistical concepts, not programming ability.
Learning From Classroom InstructionLecture There are three lectures per week, and Prof. Kpotufe’s lectures are fast-paced and cover all of the material in the course. Often, derivations will accompany definitions. Then, he will often use examples to apply the concepts to problems. After every lecture, he will post his complete notes on Blackboard, so if you miss any of the material during the lecture, you can find an almost word-for-word reproduction online. Assigned readings/texts The textbook and lectures cover almost identical material. It will be useful to at least skim the relevant sections of the textbook before the lecture on the material, as the same concepts will be discussed in lecture. The textbook is also a good source of additional example problems that Prof. Kpotufe does not have time to cover during lecture Precept Precept is held once per week to review the material covered in lecture, with a focus on applications and preparation for problem-sets. Whereas the lectures often focus on definition, notation, and intuition, the precepts take these statistical concepts and demonstrate exactly how you are expected to use them in ORF 245. All precepts cover the same material, so you can choose to attend whichever precept you like the most.
Learning For and From AssignmentsProblem-sets Problem-sets in ORF 245 are weekly and based on the material covered in that week’s lectures. On most problem-sets, there is a mix of “plug-and-chug” style questions and more theoretical questions that ask you to prove or derive relationships. Almost all of the straightforward application questions are taken from the textbook, but the theoretical questions are a mix of both textbook problems and Prof. Kpotufe’s own problems. These second set of questions can be trickier because you often won’t find similar problems in the textbook or the lectures, so it is good idea to work with others and go to office hours to get help on these problems. If you do get help on these problems, though, make sure that you understand all of the algebraic manipulations and techniques used to solve the problems because the midterm and final exam will require you to do solve similarly complex problems by yourself. Additionally, the course has programming assignments due every two weeks. These programming assignments are used to practice using the statistical ideas in more practical applications than the problem-sets. For example, a programming assignment was based off of a dataset of word frequency in emails and asked you to build a spam detector based on conditional probabilities. The programming assignments are not designed to test computer science skills, so the problems require only basic programming techniques. Because many of the problems calculate statistics on data, it will be useful to refer often to the official MATLAB documentation to use built-in functions to simplify your program when you are allowed to. While important for understanding the practical applications of the course material, the topics covered in programming assignments are not explicitly tested in exams (i.e. you will not write code for exams, but a topics covered on programming assignments might appear on exams). Tests ORF 245 has two assessments: a midterm and final exam. Past exams were not provided as Prof. Kpotufe’s exams are quite different from previous ORF 245 exams. These assessments require you to synthesize concepts in the course, so they are at a difficulty level rather higher than problem-sets. A good strategy for preparing for the exams is to review the more complex problems on problem sets. The lecture notes are also a good source for study materials. Understanding the common techniques used to derive results, such as independence and linearity of expectation, are useful on exams. Because the class is focused on a mathematical introduction to statistics, the exams will have equation sheets, so it is not useful to spend time memorizing specific probability distribution functions. Instead, you should focus your efforts on understanding the theory behind the concepts covered in the course.
External ResourcesORF 245 doesn’t require any outside resources. Between lecture notes, the textbook, office hours, and McGraw Study Hall, you can learn and get help with all of the ORF 245 material. For the programming assignments, though, it is useful to search online for a MATLAB function that calculates the statistical quantity you are interested in. Note, though, that sometimes the programming assignments specify that you write your own logic to make some calculations.
What Students Should Know About This Course For Purposes Of Course SelectionORF 245 provides an introduction to the most common statistical techniques used by statisticians, scientists, and engineers. The topics of ORF 245 can help you design better experiments and techniques to analyze data, which are skills applicable to many different disciplines. In addition, ORF 245 is a prerequisite for ORF 309, which provides an even more rigorous study of probability. ORF 245 has a consistent workload level throughout the term, with normal problem-sets due every week, programming assignments due every two weeks, and two exams.
Fundamentals of Statistics