Introduction

The goals of this course is to provide FE and FA students with the necessary probability theory background to ensure a better performance in the rest of the FE/FA programs. In particular the concepts of sigma fields or algebras are not covered in undergraduate probability courses these are fundamental for stochastic processes and for properly define random variables. The students will learn to perform probability reasoning and fundamental probability calculations to help them with the derivations in statistics, time series, and stochastic calculus.

Course Objectives

The main goal of this course is to provide FE and FA students with the necessary probability theory background to ensure a proper performance for the remaining classed in the programs. In particular, fundamental concepts of sigma fields or algebras are not covered in undergraduate probability courses. These are important topis for understanding stochastic processes, and well as for a proper introduction of random variables. We will however emphasize the applicability of probability theory, through problems and exercises. The students will learn to perform probability reasoning and fundamental probability calculations to help them with the derivations in statistics, time series, and stochastic calculus.

Textbook

[FT] Florescu, Ionut and Tudor, Ciprian A. Handbook of Probability, Wiley, 2014, ISBN 1118593146, 9781118593141. I chose to use this book as the primary textbook for two reasons. Each chapter is supposed to be more or less self contained and it contains many details that I believe are useful. Second, each chapter has a section with exercises split into two, First set of problems have solutions while the second set does not. I will assign exercises that do not have solutions but you should be working through the ones that have solutions for practice. We will be using two other textbooks.

[G] Ghahramani, Saeed Fundamentals of Probability: with Stochastic Processes, Third Edition, Chapman and Hill/CRC, Nov. 2015, ISBN 9781498755016 This is an undergraduate textbook and it is very useful for those of you who did not do a serious probability class in undergraduate. The book explains very well the basic probability distributions and concepts. I will be using exercises from the book and you should use it as a source of material and problems. Finally,

[F] Florescu, Ionut Probability and Stochastic Processes, Wiley, Oct. 2014, ISBN-13: 978-0470624555, ISBN-10: 047062455 This book has more material than the main textbook but it isn't as detailed which is why I am using the handbook as the main text. However, this book has a second part about stochastic processes which is I believe very useful for future. I am referring in particular to Markov chains and Markov processes, Poisson process and the Brownian motion.

Grading Policies

The final grade will be determined upon the student’s performance throughout the course. We will have multiple assignments, and possibly quizzes.Most of the grade will be coming from the in class midterm, as well as from the final.

Deadlines are an unavoidable part of being a professional, and this course is no exception. Course requirements must be completed and submitted on, or before the specified due date. Due dates and delivery time deadlines are defined as Eastern Time EST (local time in Hoboken, NJ). Please note, students living in distant time zones or overseas must comply with this course time and time and due date deadline policy. Avoid any inclination to procrastinate. To encourage you to stay on schedule, due dates have been established for each assignment; 20% of the total points will be deducted for assignments received 1-6 days late; assignments received more than 1 week late will receive 0 points. Please let me know - IN ADVANCE - of any issues you may have that would prevent submission being on time.

Only use the .pdf format when submitting files online. As this is a theoretical class and the due date is right before the class, generally, handwritten assignments will be collected before the class. If needed, you should be able to transform any document into a pdf file. You can use Adobe Acrobat - should be free to Stevens students as far as I know (please visit the students help desk), or use a pdf printer driver. I write all my documents in LATEXand that typesetting program produces pdf files. Word is able to produce pdf’s as well. A good online resource for latex editing is overleaf.com. If outside circumstances are affecting your ability to perform in the course, you must contact your instructor before you fall behind. Generally the grade distribution follows the following percentages -

• 25% Assignments
• 5% Attendance
• 30% Midterm
• 40% Final Exam