Introduction to Probability

MATH4008, Fall semester, 2014

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall
Office Hours: F 10-11:30am, 3:45-4:45pm
Class meeting: M W F 12:20pm - 01:15pm, 620 SWIFT

Textbooks

1. Lectures will be based on Introduction to Probability, second revised edition by Charles M. Grinstead and J. Laurie Snell
   download a PDF copy.
   Website of the textbook.
   Solutions to odd-numbered problems.
2. Recommended but not required: A First Course in Probability by Sheldon Ross.

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, moment generating functions, common discrete and continuous distributions and their properties, joint, marginal and conditional distributions, law of large numbers, and the central limit theorem.

Chapters 1-10 from the textbook [1] will be covered.

Pre-req: Multivariate calculus (MATH2063), Probability and Statistics I (STAT2037).

Grades

• Midterm: October 15, in class. Final: TBA. No makeups.
• Grading: homework/quiz 30%, midterm 30%, final 40%
• How to write homework/quiz/exam solutions:
  • Describe what are you going to do before you do it. In particular, start by stating the question that you are going to answer.
  • Use complete sentences. You should be able to read your entire solution aloud, so you need to include "transition phrases" between the formulas.
  • If you only manage to find a partial solution for a problem, state clearly what you have done and which part is missing.

Preparation for SOA/CAS Exam P/1

• A Probability Course for the Actuaries by Marcel B. Finan
  download a PDF copy (version July 8, 2014. Might differ from the latest version at authors' website in the future.)
• SOA/CAS Exam P/1 Sample Questions and Solutions.
• Sample online actuarial exams are available from http://www.saab.org/actuarialmuorg.cgi
• Offical websites of SOA and CAS.
• Website of Be an actuary.
• Actuarial Club at UC. Please contact Michael Sokol.

Tentative Schedule and Homework

We plan to cover the first 10 Chapters of the textbook [1] with the following schedule. Chapters with * are recommended but not covered in lectures. A detailed syllabus can be found here.

• Week 1 (8/24-8/30), Chapter 1.2. HW 1 (due Sep 5)
• Week 2 (8/31-9/6, Labor Day), Chapter 2.2. HW 2 (due Sep 15)
• Week 3 (9/7-9/13), Chapter 3.1.
• Week 4 (9/14-9/20), Chapter 3.1, 3.2. HW 3 (due Sep 22)
• Week 5 (9/21-9/27), Chapter 3.2, 3.3*. HW 4 (due Sep 29)
• Week 6 (9/28-10/4), Chapter 4.1. HW 5 (due Oct 6)
• Week 7 (10/5-10/11, Reading Days), Chapter 4.2, 4.3*. HW 6 (due Oct 15) Solution
• Week 8 (10/12-10/18), Chapter 5.1. Midterm Exam (Chapter 1-4). Midterm Solution
• Week 9 (10/19-10/25), Chapter 5.2, 6.1.
• Week 10 (10/26-11/1), Chapter 6.2, 6.3. HW 7 (due Nov 3)
• Week 11 (11/2-11/8), Chapter 7.1, 7.2. HW 8 (due Nov 12) Solution
• Week 12 (11/9-11/15). Sample Quiz 2 Solution
• Week 13 (11/16-11/22), Chapter 10.1, 8.1, 8.2*.
• Week 14 (11/23-11/29, Thanksgiving) Chapter 9.1, 9.2, 9.3*. HW 9 (due Dec 1)
• Week 15 (11/30-12/6), Chapter 10.1, 10.2*, 10.3.
• Week 16 (12/7-12/13), Final Exam.
  Sample problems: Midterm Exam (Solutions) Quiz 2 Sample (Solutions) Quiz 2 (Solutions) Final Sample (Solutions)

Homework include

• reading
• hand-in problems
• not hand-in problems: students may choose from
  (a) selected exercises from textbook (solutions to odd-numbered problems) and
  (b) SOA/CAS Exam P/1 Sample Questions (solutions).

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