Actuary Exam P/1 Preparation

MATH4010, Spring semester, 2016

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall
Office Hours: walk-in Fri 2:30-4:30pm, other time by appointment.
Class meeting: 4206 French Hall, Mon 5:15-6:30pm.

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.

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/CAS Exam P/1 Sample Questions (Solutions) Updated version with more recent problems until November 2015 (Solutions).
• 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.

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.

• Section 1 (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)
  
  
• Section 2 (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)
  
  
• Section 3 (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 (Jan 11 - 15): organizational meeting. Mon 5-5:30pm.


• Week 2 (Jan 18 - 22): MLK no class.


• Week 3 (Jan 25 - 29): Mon 5:15-6:30pm. 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 4 (Feb 1 - 5): Mon 5:15-6:30pm. We will first finish the combinatorial probability. Then we will and start Section 2 with frequently used distributions, and transformation of random variables.
  
  Recommended problems: 29-32, 34, 40, 71, 73.


• Week 5 (Feb 8 - 12): Mon 5:15-6:30pm. We started with transformation of random variables first last week. We will work out a few representative problems, and then review the frequently used distributions.
  
  Recommended problems: 71-75.


• Week 6 (Feb 15 - 19): We will talk a couple more problems of transformation of random variables by introducing a ``cap''. Then we shall work with a few specific types of distributions, focusing on Exponential and Poisson. Other important distributions include Uniform, Gaussian, Bernoulli, Binomial, and Geometric.
  
  Recommended problems:
  
  Transformation by a cap: 46, 47, 54, 68, 180.
  Distributions: Exponential 29, 69, 199; Poisson 30, 50, 164, 187.


• Week 7 (Feb 22 - Feb 26): We will be finishing other topics in Section 2 (Problems 29-75) soon.
  
  Recommended problems: 42, 43, 44, 52-55, 57, 58, 60, 68.


• Week 8 (Feb 29 - Mar 4): We finish Section 2 this week.


• Week 9 (Mar 7 - 11): Tues 4-5:30pm, 4622 French Hall. We start Section 3.
  
  Recommended problems: 77, 88, 90, 91, 92, 94, 100, 101, 102, 104, 105, 106, 107, 110, 111, 114, 115.


• Week 10 (Mar 14 - 18): We will keep working on Section 3.


• Week 11 (Mar 21 - 25): UC Spring break, no class.
• Week 12 (Mar 28 - Apr 1):
• Week 13 (Apr 4 - 8):

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