MATH4008-001 Fall 2021

Introduction to Probability

Course Format: Lectures M-W-F 12:20-1:15 60WCHARL 140

Homework to be collected

See Assignments on Canvas

Course Info

Instructor: Wlodek Bryc Office Hours
Textbook: Free PDF 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, Oct 1.
Exam 2: Fri, Nov 5.
Last Day to withdraw from the course: November 12.
Final Exam: Monday, December 6, 1:30-3:30 p.m.

No makeups!

Grading

Homework/Quizzes 20%, 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 turn in at least one assignment 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*
Aug 23	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
Aug 30	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
Sep 8	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	(no class on Monday)
Sep 13	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
Sep 20	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
Sep 27	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*
Oct 4	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
Oct 11	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	(no class on Monday)
Oct 18	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
Oct 25	10.5, 10.6	10.5.5, 10.5.13-10.5.15, 10.6.13, 10.6.14, 10.6.16, 10.6.19, ...	...
Nov 1	10.7-10.9 Review, Exam 2	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
Course checkpoint. The topics below may need adjustment to match the actual pace of the course
Week of	Material	Problems	*Similar from Ross*	*Remarks*
Nov 8	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
Nov 15	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
Nov 22	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	(No class Friday )
Nov 29	Review		...	Final Exam: December 6

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

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