Actuary Exam P/1 Preparation

MATH4010, Fall semester, 2016

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall
Office Hours: M 2:45-4pm, other time by appointment.
Class meeting: Wed 5:05-6:20pm, 4206 French Hall, Seminar Room.

Course description

Preparation for Actuary Exam P/1. This is a one-credit course with passing/fail grade. Key knowledge points will be reviewed and problem-solving techniques will be demonstrated. However, to make sure to be able to pass the exam, students need to put in around 150-200 hours of study/practice for preparation.

Grades

Pass/Fail grade.

Lecture Format/Contents

The following list of knowledge points is taken from the 2016 Exam 1 Syllabus. I will go over them very quickly during the lectures. Student are expected to go through them in details by oneself.

The lectures will be mostly focusing on SOA/CAS Exam P/1 Sample Questions (Solutions) Updated version with more recent problems until November 2015 (Solutions). In the parenthesis of each knowledge point are the numbers of questions related in the Sample Questions. Students are expected to solve them all as a minimum preparation of the exam. It is also recommended to work on these problems following weekly Schedule below. Recommended problems will be discussed in class. Also bring any questions you have during the study to class.

A selected number of questions will be discussed in the lectures, as indicated in Schedule below.

General Probability (1-28)

• Basic probability concepts (set functions, mutually exclusive events, addition and multiplication rules, independence of events) (1 - 5, 8 - 17, 159, 168, 179, 188, 198, 207)
  
• Conditional probability (6, 7, 24, 33, 38, 156, 169, 172, 185, 197, 201)
  
• Bayes Theorem (19-23, 25-28, 176, 181, 182, 202, 208)
  
• Combinatorial probability (141, 170, 174, 175, 177, 184, 196, 200, 210, 211)

Univariate Probability Distributions (29-75)

• Random variables (32-34, 158, 215)
  
• Expected value and other distribution parameters (44-56, 60-67, 155, 157, 166, 178, 206, 209)
  
• Moment generating function (57, 58, 130, 137)
  Percentile, mode, skewness, kurtosis, standardized random variables (59, 68-70, 194, 195)
  
• Transformation of a random variable (36, 37, 40, 71-75, 161, 167, 180, 183, 192, 205, 214)
  
• Frequently used distributions (29-31, 39, 41, 42, 43, 153, 187, 189, 190, 193, 199, 212, 213, 216)

Multivariate Probability Distributions (76-125)

• Joint probability functions and joint probability density functions (100, 110, 111, 118, 125, 171, 203)
  
• Joint cumulative distributions (77, 79, 88, 89)
  The Central Limit Theorem (80-87, 163, 186)
  Conditional cumulative distribution functions (111, 112, 119, 120, 123, 204)
  
• Moments for joint, conditional, and marginal probability distributions (96, 100, 113, 114, 115, 116, 121, 124)
  
• Joint moment generating functions (95, 98, 165)
  
• Variance and measures of dispersion for conditional and marginal probability distributions (see moments above)
  
• Covariance and correlation coefficients (99, 104-107, 160, 162)
  
• Transformations and order statistics (76, 91, 92, 94, 97, 103, 108, 109, 117, 122)
  
• Probabilities and moments for linear combinations of independent random variables (convolutions) (93, 101, 102, 164, 173)
• Commonly used multivariate distributions (90, 191)
  
  
• Mixed distributions (135, 145, 148, 149) (not explicitly required in the syllabus 2016)

Schedule

• Week 1 (Aug 24): organizational meeting.
  
  Read general tips.
  Finish a mock test before Week 2. Take the test seriously and use all 3 hours. Send me the time and scores (out of 30) before Week 2. You may use any mock test from your prepration materials, or google it online.


• Week 2 (Aug 31): Section 1.
  
  Recommended problems: 7, 13, 19, 24, 141. Here is a worksheet (recommended 14 - 17) on combinatorial probability (there are few problems from the sample questions).


• Week 3 (Sep 7): We will continue with materials from Section 1.


• Week 4 (Sep 14): Combinatorial probability.


• Week 5 (Sep 21): We start Section 2 with frequently used distributions, and transformation of random variables.
  
  Recommended problems: 29-32, 34, 40, 71, 73.


• Week 6 (Sep 28): We will continue from where we stop in Week 5.


• Week 7 (Oct 5):


• Week 8 (Oct 12): We start Section 3 (multivariate probability distributions).
  
  Recommended problems: 77, 88, 90, 91, 92, 94, 100, 101, 102, 104, 105, 106, 107, 110, 111, 114, 115.


• Week 9 (Oct 19): Conditional distribution.


• Week 10 (Oct 26): Moment generating function.


• Week 11 (Nov 2): Covariance.
  
  Recommended problems: 99, 104-107.


• Week 12 (Nov 9):


• Week 13 (Nov 15): Last class of semester.


• Week 14 (Nov 23):


• Week 15 (Nov 30):

Other preparation materials for SOA/CAS Exam P/1

• A/S/M Manual for Exam P/Exam 1 Probability, 16-th Edition, by Dr. Krzysztof Ostaszewski.
  Strongly recommended. A very popular and helpful preparation manual. The department has several copies for students to borrow. Contact Anita Swillinger for details.
• SOA Online Examp P/FM Sample.
• A Probability Course for the Actuaries by Marcel B. Finan.
  The latest version available at authors' website.
• Sample online actuarial exams are available from http://www.saab.org/actuarialmuorg.cgi
• Offical websites of SOA and CAS.
• Website of Be an actuary.
• Some general tips.

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