ISYE 2027

ISYE 2027 is an introduction to probability including the principles of probability, independence, and counting. This is then built upon with probability density functions, probability mass functions, and cumulative distribution functions of one or more discrete or continuous random variables. Topics such as convolutions, functions of random variables, and laws of large numbers are also covered. This is the first major course that ISYE majors take.

Topic List

• Basic Principles of Probability
• Conditional Probability and Independence
• Applications of Counting for Probability
• Discrete Random Variables
• Continuous Random Variables
• Expected Value and Variance
• Multiple Random Variables and Functions of them
  • Covariance and Correlation
• Limit Theorems

Class Structure

The course is lecture heavy where the professor will derive and teach each of the concepts in class. Students are then expected to complete assignments regarding each of the topics. The bulk of the grading for the class is from the exams which there are usually one or two midterms and a cumulative final.

Prerequisite Knowledge

MATH 2551 is a co-requisite for the course, you will need to know how to do a double integral and partial derivatives for the course, but this will be particularly heavy in the multiple random variables section of the course. The ISYE department recommends that if you choose to take MATH 2550 in lieu of MATH 2551 you should take it before the course instead of as a co-requisite, but as long as you are able to learn those two concepts prior to the given units you will be fine.

MATH 1553 or MATH 1554 are listed as prerequisites, but you will not need to know anything about linear algebra to be successful in the course.

MATH 1552 is also a prerequisite for the course, you will need to know how to integrate and compute an infinite series, in addition to derivatives learned in MATH 1551.

It is important to note that none of the math that will be significantly intensive within the course, just that you need to know the basics of how to do each one.

Registration

There are no linked sections that one needs to register for. The average GPA by professor gives a good indicator of the difficulty of the professor. The class is not difficult to register for overall.

Resources

• The textbook for the course is available as a free PDF online
• This website features examples and explanations for many of the course topics

Previous Semesters (optional)

Spring 2023

This semester featured two sections with Sigrun Andradottir and one section with Debankur Mukherjee. Each section met on MW and had start times at 9:30, 11:00, and 12:30. All classes were held in the IC or ISYE Main.

Sigrun Andradottir had focused particular efforts into the derivation of the concepts to ensure a strong knowledge of how each concept worked exactly. The lectures effectively taught us all that was needed for the assignments and exams. The assignments were relatively complex versions of each type of problem that was gone over in lecture and often took several hours to complete each week. The exams were much more simple versions of the assignment problems and usually mirrored the practice exams well. Handouts including the assignment solutions and practice exams with solutions were only on paper and were given out during class and office hours.