Math 4810/5310 Probability Spring 2014 Department of Mathematical and Statistical Sciences University of Colorado Denver

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1 Math 4810/5310 Probability Spring 2014 Department of Mathematical and Statistical Sciences University of Colorado Denver Instructor: Burt Simon Course dates/times: TR 12:30-1:45 Office: CU Building, Room 612 Course location: NC 1321 Office Hours: TR 3:00-4:00, or by appointment Text: Fundamentals of Probability Phone: Website: with Stochastic Processes, 3 rd ed. by Saeed Ghahramani Welcome! Probability is a fascinating and very useful mathematical theory. Math 4810/5310 is a standard introduction to probability theory. By successfully completing this course you will be ready to take courses in mathematical statistics, probabilistic modeling, stochastic processes, financial engineering, actuarial science, and various engineering fields. Please check the class web page regularly, which can be linked to from my page at math.ucdenver.edu/~bsimon. The class web page will have the weekly assignments, announcements, exam solutions, etc. I encourage students to participate in class by asking questions and answering (rhetorical) questions that I ask during class. University Course Catalog Description: Examines elementary theory of probability, including independence, conditional probability, and Bayes theorem; random variables, expectations and probability distributions; joint and conditional distributions; functions of random variables; limit theorems, including the central limit theorem. Note: No co-credit with MATH Prereq: MATH 3191; Coreq: MATH Cross-listed with MATH Semester Hours: 3 to 3 Course Overview: Introductory probability courses like this one cover axioms of probability, combinatorial probability, conditional probability, random variables (discrete, continuous, and multivariate), Expected value (mean, moments, variance, covariance, etc.), and some limit theorems (laws of large numbers, Central Limit Theorem). Course Goals and Learning Objectives: A. Overall Learning Objectives: By successfully completing this course, students will be familiar with all the basic concepts of probability theory listed in the Course Overview, and will understand how they tie together. Students will be able to calculate probabilities, expected values, etc., and be able to formulate probabilistic solutions for simple applied problems. B. Learning Outcomes: Problem Solving: Students will learn to solve problems involving uncertainty

2 that are posed as generic probability calculations, and as real-world applications of probability theory. Creative Thinking: Students will learn to distill a probability problem from a description where it may not be obvious how probability theory applies Critical Thinking: It is easy to misapply probability theory, so students will learn to apply the theory correctly. C. Major Topics: axioms of probability, combinatorial probability, conditional probability, random variables (discrete, continuous, and multivariate), Expected value (mean, moments, variance, covariance, etc.), and some limit theorems (laws of large numbers, Central Limit Theorem). D. Rationale: Probability is required as a prerequisite for many upper division math courses, like statistics, probabilistic modeling, stochastic processes; and is useful in business, engineering, and other technical fields. Course Prerequisites: Math 3191 (linear algebra) Course Credits: 3 credit hours Required Texts and Materials: Fundamentals of Probability with Stochastic Processes, third edition, by Saeed Ghahramani Course Schedule: The following schedule of course materials covered is tentative, but the dates of the exams will not change. DATES (class times) TOPICS SECTIONS FROM TEXT Jan 21, Jan 23 Axioms of probability sections Jan 28, Jan 30 Combinatorial methods sections Feb 4, Feb 6 Conditional probability sections Feb11, Feb 13 Discrete random variables sections Feb 18, Feb 20 Discrete random variables sections Feb 25, Feb 27 Review and Exam #1 March 4, March 6 Continuous random variables sections March 11, March 13 Continuous random variables sections March 18, March 20 Multi-variate distributions sections and 9.1 March 25, March 27 SPRING BREAK April 1, April 3 Multi-variate distributions sections April 8, April 10 Review and Exam #2 April 15, April 17 E(X), Var(X), Cov(X,Y), Cor(X,Y) sections April 22, April 24 Conditioning on random variables sections April 29, May 1 Sums of r.v.'s and limit theorems sections May 6, May 8 Catch-up and Review May 13, May 15 Final exam (date to be announced)

3 Assignments: I will assign homework problems from the textbook (approximately) weekly. Typically the assignment will be posted on the class web page on Tuesday, and will be due the following Tuesday. You are expected to turn in every homework assignment on time, since the purpose of the homework each week is to practice the material covered in class that week. Furthermore, homework sets will be discussed in class the day they are due, so late assignments will not receive full credit. Homework sets are expected to be written up neatly so they are easy to read (preferably using Word or Latex). Working collectively on the homework assignments is encouraged! There is no penalty, but please list the people you worked with on the papers you turn in. Basis for Final Grade: Your final grade will be based on your exam scores (two midterm exams and a final exam), weekly homework sets, and intangibles such as class participation. The intangibles can only increase your grade. Exam and homework grades will start out as numerical (e.g., between 0% and 100%), but will be curved and translated into letter grades, A+ at the top and F at the bottom. These letter grades are associated with the same numerical values that your GPA is based on, i.e., A+ = 4.3, A = 4.0, A- = 3.7, B+ = 3.3, B = 3.0, B- = 2.7, C+ = 2.3, C = 2.0, C- = 1.7, D+ = 1.3, D = 1.0, D- = 0.7, and F = 0.0. In the absence of intangibles, your final grade will be a weighted average of the letter grades on your exams and homeworks. You will get a simple homework grade, which will be the average of the individual scores, with the lowest score deleted. The weightings will be as follows: Homework (20%), Midterm Exam #1 (25%), Midterm Exam #2 (25%), Final Exam (30%). Grade Dissemination: I will try to grade homework sets within a week of when they are due, and exams by the next class after they are taken. They will be returned in class with grades on them. If you sense a mistake in my grading, please send me an , or come to my office hours to discuss. Course Policies A. Attendance: I will not take attendance, but students are expected to attend every class. You will be responsible for material I cover in class, whether or not it is in the textbook. Class participation is one of the important intangibles that can impact your grade. B. Late Work Policy: Normally I will not accept late homework sets, and I will not make arrangements if you miss an exam. Under unusual circumstances arrangements can be made. Try to give me as much lead time as possible if you know something will force you to be late with an assignment, or miss an exam. C. Extra Credit Policy: There is no extra credit in general, but students can try to raise their grades by being attentive (and participating constructively) in class, and demonstrating competence in my office hours.

4 D. Grades of Incomplete : I will follow university procedures on incompletes, i.e., they are only given in situations where unexpected emergencies prevent students from completing the course and the remaining work can be easily finished the following semester. Incomplete work must be finished the next semester or the grade automatically turns into an F. E. Group Work Policy: Students are encouraged to collaborate on homework sets, as long as they acknowledge their collaborators. There is no penalty for working together. Of course, no collaboration is allowed on exams, as that is considered cheating. F. Announcements: I will use the class web page for all communication that is meant for the whole class. Please check the page regularly. Private communication is best done by . I will typically respond within a day. G. Laptops, Cell Phones, etc.: You are free to use your devices as you see fit during class. (No phone calls or texting, of course.) The rules during exams will be announced prior to the tests. Usually my exams are open-book, open-notes, but electronic devices (calculators, computers, etc.) are not allowed. H. Civility: Students are expected to be quiet and attentive during class, although raising your hand to ask a question or make a comment is welcome and encouraged. Dishonesty: Students are expected to understand intuitively what proper ethical conduct means in the context of a college mathematics course. If you are caught cheating you could fail the class or (at least) have your grade lowered, so don t even try it. Spring 2014 CLAS Academic Policies

5 The following policies pertain to all degree-seeking students in the College of Liberal Arts and Sciences. Schedule verification: It is each student s responsibility to verify online that his/her official registration is correct: verify before classes begin and prior to the drop/add deadline. Failure to verify schedule accuracy is not sufficient reason to justify a late add or drop. Students must activate and regularly check their official student account for CU Denver business: Those who forward must check CU Denver regularly for messages not automatically forwarded. Waitlists: Students are not automatically notified if they are added to a class from a waitlist. Students are not automatically dropped from a class if they never attended, stopped attending, or do not make tuition payments. Waitlists are purged after the 1st week of classes, after which a paper Schedule Adjustment Form (SAF or drop/add form) is required. It is the student's responsibility to get the form (online or at the Advising Office, NC 4002), have it signed, deliver it to the Registrar (Annex 100) or the Student Services Center (NC 1003), and verify her/his schedule online. Late adds (after 5 February) will be approved only when circumstances surrounding the late add are beyond the student s control. This will require a written petition and verifiable documentation. Petition forms are available in NC The signature of a faculty member on a SAF does not guarantee that a late add petition will be approved. Late drops/withdrawals (after 7 April) will be approved only when circumstances surrounding the late drop have arisen after the published drop deadline and are beyond the student s control. This will require a written petition and verifiable documentation. The signature of a faculty member does not guarantee that a late drop/withdrawal petition will be approved. Tuition: Students are responsible for completing arrangements with financial aid, family, scholarships, etc. to pay their tuition prior to Census Date (5 February). Students who drop after that date are (1) financially responsible for tuition and fees, (2) academically responsible and will receive a "W" grade, and (3) are ineligible for a refund of COF hours or tuition. Graduation: Undergraduate students wishing to graduate in Spring 2014 must complete the online Graduation Application form, in the UCD Access Portal, and meet with their academic advisor to obtain a graduation application. This application must be submitted by Census Date (5 February). You can obtain an application only after meeting with your advisor. There are no exceptions to this policy. Graduate students wishing to graduate in Spring semester 2014 must complete the online Graduation Application form, in the UCD Access Portal, and have a Request for Admissions to Candidacy on file with the CU Denver Graduate School (LSC 1251) no later than 5 PM, February 5, Important Dates and Deadlines January 20, 2014: Martin Luther King Holiday. Last day to withdraw from all classes via UCDAccess and receive a refund of the $200 advance payment and all tuition. January 21, 2014: First day of classes. January 26, 2014: Last day to add or waitlist classes using UCDAccess. After this date, a Schedule Adjustment Form (SAF) is required to change, add, or drop. January 27, 2014: Last day to drop without a $100 drop charge. No adds permitted on this day. January 28 February 5, 2014: UCDAccess registration is closed; registration now requires a SAF with faculty signature. Verify your registration via UCDAccess. You are not registered for a course unless your name appears on the official roster; conversely, your name may have been added automatically from

6 the waitlist without notification, which means that you will be held responsible. February 5, 2014: Census date. 2/5/14, 5 PM: Last day to add structured courses without a written petition for a late add. This is an absolute deadline and is treated as such. This does not apply to independent studies, internships, project hours, thesis hours, dissertation hours, and modular courses. 2/5/14, 5 PM: Last day to drop a course or completely withdraw from Spring 2014 using a SAF and still receive tuition refund, minus the drop fee. After this date, tuition is forfeited and a "W" will appear on the transcript. This includes section changes. This is an absolute deadline. 2/5/14, 5 PM: Last day to request Pass/Fail or No-Credit option for a course. 2/5/14, 5 PM: Last day for a graduate student to register for a Candidate for Degree and last day for a Ph.D. student to petition for a reduction in hours. 2/5/14, 5 PM: Last day to apply for Spring 2014 graduation. If an undergraduate, you must make an appointment and see your academic advisor to apply. If a graduate student, you must complete the Intent to Graduate and Candidate for Degree forms. February 17-26, 2014: Faculty can use the Early Alert system. March 24-30, 2014: Spring Break-(no classes; campus open). April 7, 2014, 5 PM: Last day for non-clas students to drop or withdraw without a petition and special approval from the academic dean. After this date, a dean s signature is required. April 22, 2014, 5 PM: Last day for CLAS students to drop or withdraw with signatures from the faculty and dean but without a full petition. After this date, all schedule changes require a full petition. Petitions are available in NC 4002 for undergraduates and in the CU Denver Graduate School offices for graduate students. May 12-17, 2014: Finals Week. No schedule changes will be granted once finals week has started-- there are no exceptions to this policy. Commencement is May 17. May 22, 2014: Due date for faculty submission of grades (tentative). May 26, 2014: Spring final grades available on UCD Access (tentative).

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