ASRM 401/STAT 408 - Actuarial Statistics I (Spring 2020)


Instructor Partha Dey
ContactBy and from "@illinois.edu" account.
Videos Subscribe to go.illinois.edu/asrm401_ch
Q&A MWF 9:00-9:50am through Zoom Meetings.
DiscussionUsual times via Zoom Meetings led by Tavanaie Marvi Morteza.
HW upload Upload PDF files through Compass2g.
Websitehttps://faculty.math.illinois.edu/~psdey/ASRM401SP20.html.

Discussion Board and exam/hw scores are in the Compass2g website.
Textbook Probability and Statistical Inference, by Hogg, Tanis and Zimmerman, 9th edition.
A free ebook A Probability Course for the Actuaries by Marcel Finan.
Another ebook with many sample exams Study Manual for Exam P by Krzysztof Ostaszewski.

Examines elementary theory of probability, including independence, conditional probability, and Bayes' theorem; combinations and permutations; random variables, expectations, and probability distributions; joint and conditional distributions; functions of random variables; sampling; central limit theorem.

Remarks: This course (ASRM 401/Stat 408) is a basic probability course for actuarial science students; enrollment is restricted to students in the actuarial science program. The main objectives of the course are to
  • provide a general introduction to probability theory;
  • prepare for more advanced courses in statistics (in particular, Math 409 and Math 469);
  • prepare for the Actuarial Exam P.
The course covers all the material necessary for the Course 1/P Actuarial Exam, but it also includes some topics that, while not particularly relevant as exam topics (for various reasons - usually simply because they don't lend themselves to good multiple-choice exam questions), are considered parts of any standard introduction to Probability theory and prerequisites for more advanced Probability and Statistics classes. (Examples are combinatorial probabilities and the chi-square distribution.)

Instructor Partha Dey
ContactBy and from "@illinois.edu" account.
Class MWF 9:00-9:50am in 1000 Lincoln Hall
Discussion sectionsTuesdays, 2:00-2:50pm, 3:00-3:50pm and 4:00-4:50pm, 1065 Lincoln Hall. The discussion sections will begin January 29, the second week of class. The discussion sections will be led by Tavanaie Marvi Morteza.
Websitehttps://faculty.math.illinois.edu/~psdey/ASRM401SP20.html. Discussion Board and exam/hw scores are in the Compass2g site.
Office Hrs Wednesday 2-3:30pm or by appointment made via e-mail in 341A Illini Hall
Textbook Probability and Statistical Inference, by Hogg, Tanis and Zimmerman, 9th edition. We will cover the first half of the book, Chapters 1-5. The follow-up course, ASRM 402/Stat 409, usually covers the second half of this text, and chances are that you will be able to use the book for both courses. (Note that 409 is under the control of the Statistics Department and will likely be taught by statistics faculty.)
Prerequisite Math 241, 242 or 243 (Calculus III), or equivalent. While the first half of the course requires little calculus, the latter part of the course depends in an essential way on calculus, especially multi-variable calculus. Many of the problems in the latter part of the course boil down to computing multiple integrals, and you must be comfortable doing such computations.
Electronic devices No use of cell phones or other means of electronic communication during the class. In particular, no texting and no emails are allowed during the class. Laptops are Tablets are allowed only for class purposes.
Calculators For Midterm Exams and for the Final Exam, the calculator policy is the same as that used for Actuarial Exams. List of approved calculators can be found here.
DRES Please email your DRES letter to me as early as possible in the semester, so that we can make appropriate accommodations.
Actuarial links

Homework Policy Homework will be assigned weekly on Mondays on this website, to be handed in at the beginning of the Friday lecture.

You are encouraged to work together on the homework, but I ask that you write up your own solutions (and write name/s of collaborators) and turn them in separately.

Assignments dropped off in mailboxes will not be accepted; however, you can turn in an assignment in my office, 341A Illini Hall, any time before the class hour in which it is due. Late assignments will not be accepted. If you will be absent when homework is due, you must turn in your homework in advance. If you have a legitimate, documentable, excuse for missing an assignment (e.g., illness), I will mark the assignment as excused. An excused assignment will not be counted towards your homework average; by contrast, a missed assignment without a valid excuse will count as 0 points.

I will drop your two lowest hw scores and the remaining scores determine your HW grade.
Exams There will be two in-class midterm exams on Wednesdays February 26 and April 8. They will be technically comprehensive, but emphasizing recent material up to the most recent graded and returned homework assignment.

The Final Exam is comprehensive and tentatively scheduled for 8:00-11:00 a.m., Tuesday, May 12 in 1000 Lincoln Hall.
Missed examMake-up exams will not be given, unless your absence is approved by the Emergency Dean. Travel and leisure plans, even for family events, are never a legitimate reason for missing an exam. Make-up exams will not be given. If you miss an exam and have a valid excuse (e.g., illness or job/internship interview), documented with a letter from the Dean, I will mark the test as "excused". A test marked as excused is simply ignored in the grade computation, i.e., it is treated as if the test had never taken place.

Documentation: An "excused" grade must be requested within a week of the test and must be documented with a letter from the Dean. The Dean's Office is located in 300 Student Services Building, 610 East John St., phone 333-0050. Just see one of the Assistant Deans there, explain your case, and ask that they send a letter to the instructor. The people there deal with these situations all the time and have form letters that they will send to instructors if they believe you have a valid excuse (e.g., illness, but not, for example, oversleeping). One major advantage of going through the Dean's Office is that you can take care of any other missed classes at the same time by having letters sent to all of your instructors.
Grading Policy Check your grades at compass2g. Grades will be computed by a weighted average:

Discussion Section 10%
Homework 15%
Midterms
40% (20% each)
Final 35%

Minimum midterm score can be replaced by the final exam if the later is higher.

Tentative curve: A(+/-): 90-100%; B(+/-): 80-89%; C(+/-): 70-79%; D(+/-): 60-69%.

I may slightly adjust the curve later to see it fit. Two exceptions to the numerical grading for people who take all four exams: anyone who scores 95% on the Final gets an A and anyone whose scores 75% on the Final will pass. (Experience shows that these exceptions rarely make a difference.)

Homework 1 (due on 01/31): Homework 1, Solution
Homework 2 (due on 02/07): Homework 2, Solution
Homework 3 (due on 02/14): Homework 3, Solution
Homework 4 (due on 02/21): Homework 4, Solution
Midterm 1 (on 02/26): Information, Midterm 1, Solution
Homework 5 (due on 03/06): Homework 5, Solution
Homework 6 (due on 03/13): Homework 6 , Solution
Homework 7 (due on 03/27): Homework 7, Solution
Homework 8 (due on 04/03): Homework 8, Solution
Midterm 2 (on 04/08): Information, Midterm 2, Solution
Homework 9 (due on 04/17): Homework 9, Solution
Homework 10 (due on 04/24): Homework 10, Solution
Homework 11 (due on 05/01): Homework 11, Solution
Homework 12 (due on 05/06): Homework 11, Solution


Week Date Due Content






1 W Jan 22 Overview of this course. Read: Appendix D1 (review of set theory).
F Jan 24 Rules for probability and Venn diagrams. Read: Sec. 1.1.






2 M Jan 27 Examples using probability rules. Examples and Solution. Read: Sec. 1.1.
T Jan 28 Discussion Section Worksheet and Solution.
W Jan 29 Conditional probabilities. Examples and Solution. Read: Sec. 1.3.
F Jan 31 HW1 Independence. Examples and Solution. Read: Sec. 1.4.






3 M Feb 3 Bayes' Rule, Total Probability Rule. Examples and Solution. Read: Sec. 1.5.
T Feb 4 Discussion Section Worksheet and Solution.
W Feb 5 Methods of Enumeration. Examples and Solution. Read: Sec 1.2.
F Feb 7 HW2 More combinatorial problems. and Solution.
Actuarial Exam Practice Problem Set 1 and Solution to Problem Set 1.






4 M Feb 10 Discrete Random Variables. Examples and Solution. Read: Sec. 2.1, 2.2.
T Feb 11 Discussion Section Worksheet and Solution.
W Feb 12 Discrete Random Variables (contd.). Examples and Solution. Read: Sec. 2.2, 2.3.
F Feb 14 HW3 Expectation, Variance and MGF. Examples and Solution. Read: Sec. 2.2, 2.3.






5 M Feb 17 The Binomial distribution. Examples and Solution. Read: Sec. 2.4.
T Feb 18 Discussion Section Worksheet and Solution.
W Feb 19 Negative Binomial, Geometric dist. Examples and Solution. Read: Sec. 2.5.
F Feb 21 HW4 Poisson Distribution. Examples and Solution.Read: Sec. 2.6.
Actuarial Exam Practice Problem Set 2 and Solution to Problem Set 2.






6 M Feb 24 Review Problems. Review: Ch. 1 & 2.
T Feb 25 Midterm Review.
W Feb 26 Info Midterm 1
F Feb 28 Moment Generating Functions. Examples and Solution. Read: Sec. 2.3.






7 M Mar 2 Continuous Random Variables. Examples. Read: Sec. 3.1.
T Mar 3 Discussion Section Worksheet and Solution.
W Mar 4 Continuous Random Variables (contd). Examples and Solution. Read: Sec. 3.1.
F Mar 6 HW5 Uniform and Exponential Distirbuitons. Examples and Solutions. Read: Sec. 3.2.






8 M Mar 9 Gamma Distirbuiton. Examples and Solutions. Read: Sec. 3.2.
T Mar 10 Discussion Section Worksheet and Solution.
W Mar 11 Normal Distirbuiton. Examples and Solutions. Read: Sec. 3.3.
F Mar 13 HW6 Actuarial Exam Practice Problem Set 3 and Solution to Problem Set 3.






9 M Mar 16 No class. Spring Break.
W Mar 18 No class. Spring Break.
F Mar 20 No class. Spring Break.






10 M Mar 23 Examples and Solutions. Read: Chapter 3.
T Mar 24 Discussion Section Worksheet and Solution.
W Mar 25 Change of variables in random variable. Examples and Solutions. Read: Sec. 5.1.
F Mar 27 HW7 Discrete Joint Distributions. Examples and Solutions. Read: Sec. 4.1.






11 M Mar 30 Conditional PMF, Mean and Var. Examples and Solutions. Read: Sec. 4.3.
T Mar 31 Discussion Section Worksheet and Solution.
W Apr 1 Independence, Cov and Correlation. Examples and Solutions. Read: Sec. 4.2.
F Apr 3 HW8 Var, Cov, MGF and limits. Examples and Solutions. Read: Sec. 5.8-5.9.






12 M Apr 6 Review. Examples and Solutions.
T Apr 7 Discussion Section Worksheet and Solution.
W Apr 8 Info Midterm 2
F Apr 10 Review of Double Integral. Examples and Solutions.






13 M Apr 13 Continuous Joint Distributions. Examples and Solutions. Read: Sec. 4.4.
T Apr 14 Discussion Section Worksheet and Solution.
W Apr 15 Contd. Examples and Solutions. Read: Sec. 4.4.
F Apr 17 HW9 Contdional Density and Examples. Examples and Solutions. Read: Sec. 4.5.






14 M Apr 20 Actuarial Exam Practice Problem Set 4 and Solution to Problem Set 4.
T Apr 21 Discussion Section Worksheet and Solution.
W Apr 22 Transformation of 2 rvs. Examples and Solutions. Read: Sec. 5.2.
F Apr 24 HW10 Several Independent rvs. Examples and Solutions. Read: Sec. 5.3.






15 M Apr 27 More on Normal Distributions. Examples and Solutions. Read: Sec. 5.4.
T Apr 28 Discussion Section Worksheet and Solution.
W Apr 29 Central Limit Theorem. Examples and Solutions. Read: Sec. 5.6.
F May 1 HW11 Examples of Normal Approximation. Examples and Solutions. Read: Sec. 5.7.






16 M May 4 Linear combination of Normal rvs. Examples and Solutions. Read: Sec. 5.5.
T May 5 Discussion Section Worksheet and Solution.
W May 6 HW12 Review. Examples and Solutions.






17 T May 12 Final exam 8:00-11:00am