Applied Mathematics and Statistics 553.420/620
Probability
Spring 2024 (4 credits, EQ)
COURSE DESCRIPTION (from the course catalog)
Probability and its applications, at the calculus level. Emphasis on techniques of application rather than on rigorous mathematical demonstration. Probability, combinatorial probability, random variables, distribution functions, important probability distributions, independence, conditional probability, moments, joint distributions, covariance and correlation, conditional distributions, conditional expectation, conditional variance, ordered statistics, exchangeability, inequalities, limit theorems. Students initiating graduate work in probability or statistics should enrollin EN.550.620. Auditors are not permitted. Recommended Course Background: one year of calculus and mathematical maturity; Co-requisite: multivariable calculus.
Prerequisites
(AS.110.108 [+] AND AS.110.109 [+]) OR (AS.110.106 [+] AND AS.110.107 [+])
Statistics Sequence restriction: students who have already completed EN.550.430 [+] may not register
REFERENCES
My personal course notes will be provided.
(Not required) Sheldon Ross,A First Course in Probability, Pearson Publishing, 9th edition or later. My personal course notes were written around the 9th edition of this textbook. The problems and theoretical exercises are very good in this textbook (some have answers in the back of the book) and each chapter has a chapter test with full solutions in the back of the book.
Gabe Gormezano, Intuition to Probability**, book (in progress). Written by one of our undergraduates a PDF version of this book will be posted to Canvas for your enjoyment. It is an excellent source for problems/exercises to expand your knowledge of the subject.
COURSE ASSESSMENT & GRADE ASSIGNMENT
Weekly homework assignments (25%) – expect a homework assignment* each week without a midterm
*some homework will be posted but will not be collected for grade, Two (2) midterms (25% each),last exam – noncumulative (25%)
Cut-offs for letter grades to be posted after the grading of each midterm and after last homework.
IMPORTANT DATES
Thursday, FEB. 29, Midterm 1 @ 6:00 in a room to be announced. Thursday, APR. 04, Midterm 2 @ 6:00 in a room to be announced. Last exam: MAY 14 @ 2:00-3:30. Location to be announced.
These exam dates are mandatory. Plan to take these midterms at these times. If you happen to miss a midterm, you may be eligible for an incomplete in this course, which you can plan to make-up in January. A university verifiable excuse with valid documentation may be necessary.
OPPORTUNITIES FOR BONUS POINTS
Below I list ways that students can be awarded additional points this semester. The actual points awarded have not been fully determined or are not being disclosed. I consider these as incentives, and no one will be punished for not taking advantage of these opportunities.
. Homework solutions submitted/typeset completely in LaTeX may receive additional points per assignment. Students will not be deducted points for not submitting LaTeX’d solutions.
. On exams, there is sometimes a bonus part to a question that will grant a few extra points if answered correctly.
. By attending and participating in your assigned section, you may receive a bonus to your final
grade if you have perfect/near perfect attendance and participate substantially by answering and asking many questions. If you have perfect/near perfect attendance, but participate more
inconsistently, you may receive a small bonus to your final grade. There is no penalty for a lack of attendance/participation.
EXTRA CREDIT OPPORTUNITIES
Other than the methods listed in the section above, there are no other opportunities to gain extra credit. Please do not ask myself or any TAs for such opportunities.
MIDTERMS
. To the extent possible midterm examinations will be non-cumulative; however, since this course builds on itself and introduces definitions and ideas continually, you may be required to recall an idea from an earlier part of the course on midterm examinations.
. Midterm content will either be made clear in Lectures, Canvas, or by email communication – see also the tentative schedule on last page of this syllabus. Generally, homework assignments, in-class examples, related book examples/problems, lecture content, old midterms/problems,
exercises from recitation sections are all fair-game.
. Exams will be administered IN-PERSON. Students will have a fixed amount of time to complete the exam (typically 75 minutes). If you’re allowed extended time for midterms, I need you to send me this documentation immediately.