MATH4008-001 Spring 2021

# Introduction to Probability

Course Format: Online Synchronous M-W-F 11:15am-12:10 on Webex

### Homework to be collected via Canvas

• TBA due Sunday

### Course Info

Instructor: Wlodek Bryc Office Hours
Textbook: A Probability Course for the Actuaries by Marcel B. Finan (local copy)
You may also read the corresponding material from Sheldon Ross A First Course in Probability (9th Edition) Pearson, ISBN-13: 978-0321794772 or ISBN-10: 032179477X which was used in Fall 2020.

### Exams and important dates

• Exam 1: Fri, Feb 19 during class time
• Exam 2: Fri, March 19 during class time
• Last day to withdraw: April 2
• Final Exam: Th, April 22, 9:45 - 11:45 a.m.
No makeups!

Homework/Quizzes 10%, Class Participation (Polls) 10%, Exams 25% each, Final 30%
Course Ave = .2 Hwk and Quiz Ave % + .5 Exams ave % + .3 Final exam %

Grading scale: Course Ave above 93% is A, 90% is A-, 80% is B-, 70% is C-, 60% is D-.

Withdrawal policy: You will need to take at least one Poll to confirm your participation in the class.

#### Course description

This course is an introduction to mathematical probability suitable as preparation for actuarial science, statistical theory, and mathematical modeling. Topics include: review of general probability rules, conditional probability and Bayes theorem, discrete and continuous random variables, standard discrete and continuous distributions and their properties, with emphasis on moments and moment generating functions, joint, marginal and conditional distributions, transformations of variables, order statistics, and the central limit theorem. Includes practice for the SOA/CAS Actuarial Exam P/1. Credit Level:U Credit Hrs:3 Pre-req: See your college advisor for details. Baccalaureate Competency: Critical Thinking.

### How to write homework solutions

For homeworks to be turned in:
• Start by summarizing what is given and what is the question that you are going to answer.
• Explain your work. Describe what are you going to do before you do it.
• Use complete sentences. You should be able to read your entire solution aloud, so you need to include "transition phrases" between the formulas.

## Homework

If the assigned homework is too challenging, try to solve first the easier/earlier problems as a warmup.
 Week of Material Problems Similar from Ross Remarks Jan 11 Ch 1, Ch 2 1.2.3, 1.2.5-1.2.7, 1.2.9, 1.2.14, 1.2.17, 1.2.21-1.2.23, 2.1.19, 2.1.20, 2.2.18, 2.2.20 2.3.10, 2.3.17, Ross: 1.1-1.5 Jan 18 Ch 4 4.1.4, 4.1.14, 4.1.15, 4.1.17, 4.1.21-4.1.23 4.2.6-4.2.17, 4.3.8, 4.3.9, 4.3.18-4.3.20 Ross: 2.1-2.5 (no class on Monday) Jan 25 Ch 5 5.1.1-5.1.3, 5.1.17, 5.1.18, 5.2.1-5.2.9, 5.2.12-5.2.21, 5.3.2-5.3.4, 5.3.8, 5.3.15-5.3.20 Ross: 3.1-3.5 Feb 1 Ch 6 6.1.4, 6.1.8, 6.1.17-6.1.19, 6.2.17, 6.2.18, 6.3.2, 6.3.9, 6.3.14, 6.3.20, 6.3.21, 6.4.5, 6.4.6, 6.4.19, 6.5.1, 6.5.2, 6.5.19, 6.5.20 Ross: 4.1-4.5 Feb 8 7.1-7.6 7.1.20, 7.2.4-7.2.6, 7.2.20, 7.2.21 7.3.2, 7.3.9, 7.4.8-7.4.10, 7.4.15, 7.4.19-7.4.24, 7.5.9, 7.6.9, 7.6.18-7.6.22 Ross: 4.6-4.9 Feb 15 7.7, 7.8 Review, Exam 1 7.7.7, 7.7.13, 7.7.21, 7.8.19-7.8.21 Ross: 4.8, 4.9 Course checkpoint. The topics below may need adjustment to match the actual pace of the course Week of Material Problems Material from Ross Remarks Feb 22 Ch 8, 9.1-9.6 8.1.16, 8.1.17, 9.1.10-9.1.13 9.1.19-9.1.23 9.2.8-9.2.17 9.3.5, 9.3.8, 9.3.9 9.4.14-9.4.24, 9.5.7-9.5.9, 9.5.13-9.5.17, 9.5.21-9.5.27, 9.6.7, 9.6.14-9.6.23 Ross: 4.10, 5.1-5.4 Mar 1 9.7-9.10 9.7.6, 9.7.7, 9.8.8-9.8.32, 9.3.7, 9.9.10, 9.9.11, 9.10.9-9.10.13, 9.10.21 Ross: 5.5-5.7 March 8 10.1-10.4 10.1.5, 10.1.7-10.1.11, 10.2.4-10.2.20, 10.3.9-10.3.15, 10.3.18-10.3.20, 10.4.1, 10.4.3, 10.4.4 Ross: 6.1, 6.2, 6.6 March 15 10.5, 10.6 Review, Exam 2 10.5.5, 10.5.13-10.5.15, 10.6.13, 10.6.14, 10.6.16, 10.6.19, ... ... Course checkpoint. The topics below may need adjustment to match the actual pace of the course Week of Material Problems Similar from Ross Remarks March 22 10.7-10.9 10.7.11, 10.7.13-10.7.15, 10.7.21, 10.7.22, 10.8.8-10.8.18, 10.8.21, 10.9.13, 10.9.14 Ross: 6.3-6.5, 6.7 (No class We, Mar 24) March 29 11.1-11.4 11.1.11-11.1.25, 11.2.10-11.2.14, 11.2.20-11.2.25, 11.3.6, 11.3.13, 11.4.6, 11.4.8, 11.4.10-11.4.12, 11.4.20-11.4.25 Ross: 7.2, 7.4, 7.5 April 5 11.5-11.6 11.5.21-11.5.25, 11.6.1-11.6.3, 11.6.7-11.6.12, 11.6.17-11.6.23 Ross: 7.5.2 April 12 12.1-12.3 12.1.6, 12.1.13, 12.1.18-12.1.20, 12.2.5, 12.2.7, 12.2.8, 12.2.16, 12.2.17, 12.2.21-12.2.26 12.3.10-12.3.23 Ross: 7.7, 7.8, 8.3 April 19 Review ... Final Exam: Th, Apr 22

### Alternative homework from Ross from Fall 2020 class of Dr. M. Peligrad

P=problem T=Theoretical exercises.
• Chapter 1: 1,2,3,5,8,9,12,14,15, 16,18
• Chapter 2: 1,2,3,6,7,8,9,11,12,15(a,e), 21(a), 23, 29, 36 (a), 41, 46, 47
• Chapter 3: Problems 2,5,8,12, 14(a),17,18,21,23,26,30,50,55,59(a,b), 66(a)
• Chapter 4: (first part) P: 1,2,5,17,19,21(b),25,28,35,37 T: 2,3,7,8
• Chapter 4: (second part) P: 33,39,40,42,51,52,54,55,57,58,63,64,71,82,83, T:16, T27
• Chapter 5: P: 1, 2, 4, 6, 7,8, 11, 13, 14, 15, 16, 17, 18, 19, 23, 25, 32, 33, 36, T: 2, 3, 5, 9
• Chapter 6: P:2, 4, 8, 9, 10, 13, 19, 20, 21, 23, 27, 29, 32, 33, 34, 35, 40, 41, 42, 55, 56, 58
• Chapter 7: P: 1, 4, 6, 26, 30, 31, 33, 38, 39, 40, 45, 48, 49,50, 51, 52, 53, 57, 58, 75, 76 T: 1, 6, 7, 19, 22, 46, 48, 49, 50
• Chapter 8: P: 2, 3, 4, 6, 7, 8, 13, 15

## Classroom Procedures/Policies

Communication is a bottle-neck in online classes. Use chat during Webex meetings. Use email, or leave a telephone message outside of class.

For Technology assistance, use Canvas support listed under their Help menu. Contact the IT@UC Service Desk for general IT issues.

The University Rules, including the Student Code of Conduct, and other documented policies of the department, college, and university related to academic integrity will be enforced. Any violation of these regulations, including acts of plagiarism or cheating, will be dealt with on an individual basis according to the severity of the misconduct.

## Academic Integrity Policies for Spring 2021

### Allowed

All assignments, homeworks, projects, exams, quizes are open book and open notes. However, in this class we want to learn how to solve questions in a timely manner, so do not over-rely on these resources.

You may discuss your homeworks or projects with other students, provided any help you received is described and acknowledged in your submission, and you did not merely copy their work.

### Disallowed

You may not communicate with other people while taking online quizzes or online exams.

You may not submit someone's work.

Presenting some else work as your own, whether you paid for it, got it for free, or just found somewhere, is simply not acceptable. In particular, you may not hire others to take your exams for you, or to purchase your submissions. Submitting as your own a work done by a tutor also falls under plagiarism and is not acceptable.

Students are expected to review and follow the UC Faculty Senate policies on Attendance, Class Cancellation, Academic Integrity, Accessibility, Title IX , Counseling Services

## Safety

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#### Syllabus is subject to change

This syllabus may be updated with additional information as it becomes available. Please refresh your browser to make sure that the updates are visible. Revision date appears at the top and at the bottom of this page.