STA256 AL Fall2021 courseoutline PDF

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STA256H5 - Probability and Statistics I Fall 2021 Course Outline

Lecture Times:

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LECTURES:

LEC9101, Tuesday, 12:00 - 13:00

LEC9101, Thursday, 12:00 - 14:00 LEC9102, Tuesday, 13:00 - 15:00

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LEC9102, Thursday, 14:00 - 15:00

Friday, 18:00 - 19:30 (Fridays are reserved for Test/Quizzes for ALL sections. More details below.) Instructor: Al Nosedal

Office Location: DH 3030 (Deerfield Hall) Telephone: (905) 828 - 3812.

E-mail Address: [email protected] Office Hours: Fridays, 16:30 - 19:30 (except on test days) or by appointment. (Office hours may change before tests)

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Course Web Site: https://q.utoronto.ca TUTORIALS: Tutorials begin the week of September 13th. Office Hours and Email Addresses: TA contact information and office hours will be announced in the Quercus website.

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COURSE DESCRIPTION (Formerly STA257H5) This course covers probability including its role in statistical modeling. Topics include probability distributions, expectation, continuous and discrete random variables and vectors, distribution functions. Basic limiting results and the normal distribution presented with a view to their applications in statistics. [36L, 12T] Prerequisites: MAT134Y5/135Y5/137Y5/75%+ in MAT133Y5 Corequisite: MAT233H5 for students with MAT133. For others, MAT232 is strongly recommended. Exclusion: STA257H5, 257H1, STAB52H3; ECO227Y5 Distribution Requirement: SCI. Students who lack a pre/co-requisite can be removed at any time unless received explicit waiver from department.

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DELIVERY MODE DESCRIPTION Online Synchronous: Online attendance is expected at a specific time for some or all course activities, and attendance at a specific location is not expected for any activities or exams. TEXTBOOK Mathematical Statistics with Applications 7E, by Wackerly, Mendenhall and Scheaffer, ISBN- 13:978-0-495-11081-1 You can purchase textbook through this link: Digital: https://www.campusebookstore.com Print: Bookstore has some used copies available. ADDITIONAL REFERENCES • John E Freund’s Mathematical Statistics edited by Miller and Miller. • Modern Mathematical Statistics, by Devore and Berk. • Introduction to Mathematical Statistics, by Hogg and Craig. STA256 H5F Fall 2021 - COURSE OUTLINE

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STATISTICAL COMPUTING This course uses R. R is an open-source computing package which has seen a huge growth in popularity in the last few years. R can be downloaded from https://cran.r-project.org ASSESSMENT AND DEADLINES Type Term Test 1 Term Test 2 Quizzes Final Exam

Due date Friday, October 08 Friday, November 05 Weekly (starting 2nd week) December - Date TBA

Weight 21% 21% 8% 50%

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TESTS (more details)

• The term tests are held from 18:00 to 19:30 on the test dates. There is no extra time for late entrants. • NO accommodations will be made for assessments missed during these times.

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• All the exams will be held on Quercus. Submission via another tool such as email will not be accepted. • As this is an online course and all assessments must be submitted through Quercus, it is the STUDENT’S responsibility to ensure they have a reliable internet connection. • Late submissions will not be accepted.

• NO makeup will be given for any missed term test. The mark of any missed term test will be substituted based on the final exam. • The final exam covers material from the entire course.

Missed Final Exam Policy: Students who cannot complete their final examination due to illness or other serious causes must file an online petition within 72 hours of the missed examination. Late petitions will NOT be considered. Students must also record their absence on ACORN on the day of the missed exam or by the day after at the latest. Upon approval of a deferred exam request, a non-refundable fee of $70 is required for each examination approved. With regard to remote learning and online courses, UTM wishes to remind students that they are expected to adhere to the Code of Behaviour on Academic Matters regardless of STA256 H5F Fall 2021 - COURSE OUTLINE

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the course delivery method. By offering students the opportunity to learn remotely, UTM expects that students will maintain the same academic honesty and integrity that they would in a classroom setting. Potential academic offences in a digital context include, but are not limited to: Remote assessments: 1. Accessing unauthorized resources (search engines, chat rooms, Reddit, etc.) for assessments. 2. Using technological aids (e.g. software) beyond what is listed as permitted in an assessment. 3. Posting test, essay, or exam questions to message boards or social media. 4. Creating, accessing, and sharing assessment questions and answers in virtual “course groups.” 5. Working collaboratively, in-person or online, with others on assessments that are expected to be completed individually.

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All suspected cases of academic dishonesty will be investigated following procedures outlined in the Code of Behaviour on Academic Matters. If you have questions or concerns about what constitutes appropriate academic behaviour or appropriate research and citation methods, you are expected to seek out additional information on academic integrity from your instructor or from other institutional resources.

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QUIZZES There will be 11 quizzes given during the course. They will generally consist of problems similar to homework problems or examples worked out in class. Quizzes will be posted every Friday (starting second week), approximately at noon and will be available for 24 hours. Quizzes must be completed individually. You may have general discussions about the quizzes with other students, however, the work you submit must be your own. You may seek guidance from the instructors or TAs with questions, however, we cannot solve the problems for you. Late quizzes are not accepted. Your lowest quiz mark is dropped and the remaining quizzes are worth 8% of your final grade. Missed quizzes earn a mark of zero, no exceptions. Medical certificates and/or other valid documentation are not accepted. Late Quiz Policy: Quizzes must be submitted by the due dates. Late quizzes will not be accepted. HOMEWORK Homework and readings will be assigned but not graded. However, homework problems will form the basis for tests and final exam, and will be essential to your understanding of the topics covered in class. You are encouraged to work together in groups on homework to solidify your knowledge of the material. Assigned homework problems will be listed on our webpage. TUTORIALS Tutorials are held every week and begin the week of September 13th. Tutorials will be used for your TA to review topics and take up homework problems. STA256 H5F Fall 2021 - COURSE OUTLINE

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EMAIL POLICY Email is most appropriate for personal questions. Before you send an e-mail, make sure that you are not asking for information that is already on the course outline/ website/announcements, or questions about the course material that are more appropriately discussed during office hours. If you do not get a response, this may be why. If your question is conceptual and does not require calculations or an elaborate answer, you can ask by email. Any questions regarding the tutorials should be addressed to your TA. For all other matters, contact the instructor. Please email the instructor and TAs using your *@utoronto.ca address. The subject line should contain the course number, lecture section number, and a relevant subject (indicating what the email is about). Be sure to include your full name and student number in the body of the message. You will not get a response if you email from other email addresses or do not follow the email policy. OFFICE HOURS There are plenty of office hours at various days/times offered by the TAs and instructor. You may also book an appointment with the instructor if you are unable to attend the regular office hours or need extra help. The TAs and instructor are here to help you! Ask questions and let the instructor know if there are any concerns. COPYRIGHTS

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All course materials are copyrighted. If they are from the textbook, the copyright belongs to the textbook publisher. If they are provided by an instructor (for example, lecture notes, computer code, assignments, tests, solutions) the copyright belongs to the instructor. Distributing materials online or sharing them in any way is a copyright violation and, in some situations, an academic offence. ACCESSABILITY NEEDS The University of Toronto Mississauga is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom, or course materials, please contact AccessABILITY Resource Center as soon as possible: http://www.utm.utoronto.ca/accessability. STUDENT RESPONSIBILITIES • It’s up to you to know all course policies and important dates - read the course outline. It’s up to you to know about any important announcements - these will come to your inbox. Check Quercus regularly! Check your *@utoronto.ca inbox regularly! • You’re responsible for your own learning. We’re happy to help you learn, but in the end it’s up to you! Use office hours early, and use them often. Make an appointment with the professor. Keep asking questions until you’re satisfied. Ask about big STA256 H5F Fall 2021 - COURSE OUTLINE

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concepts or small details there is no such thing as a stupid question! Always take advantage of extra help and don’t wait until it’s too late! • You must follow the U of T code of Behaviour this means that cheaters will be prosecuted. The Academic Regulations of the University are outlined in the Code of Behaviour on Academic Matters. You are expected to be familiar with, and to abide by, all components of the Code of Behaviour on Academic Matters. Full details can be found online at http://www.governingcouncil.utoronto.ca/policies What you get out of the course depends on what you put into the course! INSTRUCTOR RESPONSIBILITIES • Lectures will be clearly presented, organized, and have plenty of examples.

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• Extra help, remedial and acceleration, is always available - in office hours, by appointment, and by email. • Your emails will be answered in a timely fashion.

• Every student in the class will be treated with fairness and respect. Students who wish to excel are encouraged to consult regularly with the instructor. Students who abuse the U of T code of behavior will be dealt with appropriately.

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COURSE TOPICS

Probability - Chapter 2 2.2 Probability and Inference 2.3 A Review of Set Notation 2.4 A Probabilistic Model for an Experiment: The Discrete Case 2.5 Calculating the Probability of an Event: The Sample-Point Method 2.6 Tools for Counting Sample Points 2.7 Conditional Probability and the Independence of Events 2.8 Two Laws of Probability 2.9 Calculating the Probability of an Event: The Event-Composition Method 2.10 The Law of Total Probability and Bayes’ Rule 2.11 Numerical Events and Random Variables 2.12 Random Sampling

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Discrete Random Variables and Their Probability Distributions - Chapter 3 3.1 Basic Definition 3.2 The Probability Distribution for Discrete Random Variables 3.3 The Expected Value of a Random Variable or a Function of Random Variable 3.4 The Binomial Probability Distribution 3.5 The Geometric Probability Distribution 3.6 The Negative Binomial Probability Distribution 3.7 The Hypergeometric Probability Distribution 3.8 The Poisson Probability Distribution 3.9 Moments and Moment-Generating Functions 3.10 Probability Generating Functions (subject to time availability)

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Continuous Random Variables and Their Probability Distributions - Chapter 4 4.2 The Probability Distribution for Continuous Random Variable 4.3 The Expected Value for Continuous Random Variable 4.4 The Uniform Probability Distribution 4.5 The Normal Probability Distribution 4.6 The Gamma Probability Distribution 4.7 The Beta Probability Distribution 4.8 Some general Comments 4.9 Other Expected Values 4.10 Chebyshev’s Theorem 3.11 Chebyshev’s Theorem

Multivariate Probability Distributions - Chapter 5 5.2 Bivariate and Multivariate Probability Distributions 5.3 Marginal and Conditional Probability Distributions 5.4 Independent Random Variables 5.5 The Expected Value of a Function of Random Variables 5.6 Special Theorems 5.7 The Covariance of Two Random Variables 5.8 The Expected Value and Variance of Linear Functions of Random Variables 5.11 Conditional Expectations

6.1 6.2 6.3 6.4 6.5 6.6

Functions of Random Variables - Chapter 6 Introduction Finding the Probability Distribution of a Function of Random Variables The Method of Distribution Functions The Method of Transformations The Method of Moment-Generating Functions Multivariable Transformations using Jacobians (subject to time availability)

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Sampling Distributions and the Central Limit Theorem - Chapter 7 7.1 Introduction 7.3 The Central Limit Theorem (subject to time availability)

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Homework Problems Section 2.3 Exercises 2.1, 2.3, 2.5, 2.7 Section 2.4 Exercises 2.9, 2.11, 2.13, 2.15, 2.17, 2.19 Section 2.5 Example 2.4 Exercises 2.25, 2.27, 2.29, 2.31, 2.33

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Section 2.6 Exercises 2.35, 2.37, 2.39, 2.41, 2.43, 2.51, 2.53, 2.55, 2.61, 2.63 Section 2.7 Exercises 2.71, 2.73, 2.75, 2.77, 2.79, 2.83.

Section 2.8 Exercises 2.85, 2.87, 2.89, 2.91, 2.95, 2.101.

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Section 2.9 Exercises 2.111, 2.115, 2.117, 2.121. Section 2.10 Exercises 2.125, 2.129, 2.135. Section 3.2 3.1, 3.3, 3.5, 3.7, 3.9

Section 3.3 3.13, 3.15, 3.17, 3.19, 3.21, 3.23, 3.25, 3.27, 3.31, 3.33. Section 3.4 Exercises 3.39, 3.41, 3.43, 3.45, 3.49, 3.53 Section 3.5 Exercises 3.67, 3.68, 3.69, 3.73, 3.79, 3.81. Section 3.6 Exercises 3.91, 3.93, 3.97

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Section 3.7 3.103, 3.105, 3.109, 3.113 Section 3.8 3.121, 3.125, 3.127, 3.135, 3.137, 3.139 Section 3.9 3.145, 3.147, 3.149, 3.151, 3.153, 3.155 Section 4.2 Exercises: 4.1, 4.3, 4.5, 4.7, 4.9, 4.11, 4.13, 4.15, 4.17, 4.19

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Section 4.3 Exercises: 4.21, 4.23, 4.25, 4.27, 4.29, 4.31, 4.33 a) and c). Section 4.4 Exercises: 4.39, 4.41, 4.43, 4.45, 4.49, 4.51, 4.53.

Section 4.5 Exercises: 4.59, 4.61, 4.63 a), 4.65, 4.69, 4.71, 4.73, 4.75, 4.77

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Section 4.6 Exercises: 4.89, 4.91, 4.93, 4.95, 4.97 Exercises: 4.96, 4.105 a), 4.109

Section 4.7 Exercises: 4.123 a), 4.124 a), 4.125, 4.127, 4.129, 4.131, 4.133 a), b), c). Section 4.9 Exercises: 4.137, 4.139, 4.141, 4.143. Section 4.10 Exercises: 4.149, 4.150 Section 5.2 Exercises: 5.1, 5.7, 5.9, 5.11. Section 5.3 Exercises: 5.19, 5.25, 5.27.

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Section 5.4 Exercises: 5.45, 5.51, 5.53. Section 5.5 and 5.6 Exercises: 5.72, 5.75, 5.77, 5.79. Section 5.7 Exercises: 5.89, 5.92, 5.93, 5.95.

Section 5.11 Exercises: 5.133, 5.136, 5.157. Section 6.3 Exercises: 6.3, 6.7, 6.11, 6.13. Section 6.4 Exercises: 6.25, 6.27, 6.29.

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Section 5.8 Exercises: 5.103, 5.106.

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Section 6.5 Exercises: 6.37, 6.39, 6.40, 6.41, 6.43, 6.49, 6.57, 6.59. Section 6.6 Exercises: 6.63, 6.65 (a, b, and c), 6.71

Section 7.3 Exercises: 7.43, 7.45, 7.47, 7.49, 7.51, 7.57.

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