Steve Sawin
MA 354
MA 354 Actuarial Problem Solving – Syllabus
Spring 2016 (1 credit)
• Instructor: Stephen Sawin, BNW 109, x2573. My office hours are provisionally Monday 12:30 -1:20, Wednesday 11:00-11:50, Thursday 12:30-1:20
• Class: 354A W 12:00-12:50 in BNW 137.
• We will be developing mathematical problem solving skills with a focus on the Society
of Actuaries’ Exam P, as well as tools for quantitative risk assessment. Prerequisite
is MA 351 Probability and Statistics I and corequisite is MA 352 Probability and
Statistics II.
• Required Book: John E. Freund’s Mathematica Statistics 7th Edition by Miller and
Miller or the current MA 351/352 text.
• Other References:
1. A First Course in Probability (8ed), 2009, by Ross, S.M., Chapters 18.
2. Mathematical Statistics with Applications (7ed), 2008, by Wackerly, D., Mendenhall III, W., Scheaffer, R., Chapt. 1-7.
3. Probability for Risk Management (2ed), 2006, by Hassett, M. and Stewart, D.,
Chapt. 111.
4. Probability and Statistical Inference (8ed), 2009, by Hogg, R.V. and Tanis, E.A.,
Chapt. 15.
5. Probability and Statistics with Applications, 2010, by Asimow, L. and Maxwell,
M.
6. Probability: The Science of Uncertainty with Applications to Investments, Insurance and Engineering, 2001, by Bean, M.A., Chapters 19.
7. Tables given for actuary exam
8. Risk and Insurance
9. BeAnActuary.com
10. Online seminars by The Infinite Actuary (theinfiniteactuary.com)
11. The study materials from Actex Publishing (actexmadriver.com).
• Students planning on taking the first actuarial exam should obtain an approved Texas
Instruments Calculator [BA-35, BA II Plus, BA II Plus Professional, TI-30Xa, TI-30X
II (IIS Solar or IIB Battery), or TI-30XS MultiView (or XB battery)] and practice
doing problems with the calculator.
Topics Covered:
1. General Probability:
(a) Set notation and operations
(b) Basic probability
(c) Mutually exclusive
(d) Independence
(e) Combinatorial probability
(f) Conditional probability
(g) Bayes Theorem/Total Law of Probability
2. Univariate Probability Distributions including Binomial, Negative Binomial, Geometric, Hypergeometric, Poisson, Uniform, Exponential, Gamma and Normal
(a) Probability functions and density functions
(b) Mode, median, percentiles and moments
(c) Variance and measure of dispersion
(d) Moment generating functions
(e) Transformations
3. Multivariate probability distributions including Bivariate normal Joint probability
functions and density functions
(a) Joint cumulative distribution functions
(b) Central limit theorem
(c) Conditional and marginal probability distributions
(d) Moments for joint, conditional and marginal probability distributions
(e) Joint moment generating functions
(f) Variance and measures of dispersion for conditional and marginal distributions
Covariance and correlation
(g) Transformations and order statistics
(h) Probabilities and moments for linear combinations of independent random variables
Grading:
• Homework: You will complete the homework and then fill out and submit (emailed
to before class (12pm each Wednesday)) your self-assessed grades for each of the
homework problems assigned for the week. The 5 lowest homework problem scores
will be dropped at the end of the semester. If you miss a class you will receive a 0 for
the two problems that you were assigned to present. You should try working on each
problem for at least a half hour before looking at the solutions. The grading scheme
for each homework problems will follow this rubric:
– 10 points: Complete and correct solution without using the solutions
– 8 points: Problem is solved completely, but only after looking at the solutions
– 7 points: Significant progress made towards the solution (at least half of the
problem solved) but the entire solution is not complete even after looking at the
solution
– 5 points: Minor progress made toward the correct solution (less than half of the
problem is solved) but the entire solution is not complete even after looking at
the solution
– 0 points: No progress made, problem is skipped or student was absent and did
not present problems
• Take-home Exams: There will be two take-home, closed book exams consisting of
10 actuarial exam problems. The first exam will be distributed on March 16 and will
be due March 23. The second exam will be distributed on April 20 and due April 27.
These exams are closed book/closed notes. You are not allowed to use any outside
sources, notes, homeworks or to work with other people on these problems.
• Final Exam: Since this is a one-credit seminar course, there will be no final exam.
The students course grade will be determined by their homework grades and the
take-home exams.
• Course Grade Calculation: I will average these three numbers:
– Average homeworks, each as a percentage of total possible, dropping five lowest
– Test I as a percentage of total possible points
– Test II as a percentage of the total possible points,
– . . . 80 ≤ x < 83 = B−, 83 ≤ x < 87 = B, 87 ≤ x < 90 = B+, etc.
Honor Code and Academic Honesty
I had to fail roughly one student per semester for cheating before I started my current academic honesty policy, and it has been a very unpleasant experience for me and a
very damaging experience for the students involved. I have also regularly experienced a
widespread low level of failure to live up to reasonable standards of academic honesty. This
stands in dramatic contrast to my impression of Fairfield students in almost every other
context: As a group you are exceptionally thoughtful and committed to ethical behavior.
I believe that much of the problem is a combination of expectations from us (University,
faculty) that are fuzzy, indistinct and not entirely serious and a convenient self-deception
from many of you (students) that allows you to think reasonable standards of ethical behavior somehow do not count in this situation. For this reason I have learned to give you
extremely clear expectations and commit to them fully.
Consequences
If an infringement of the following rules is a minor matter, you will receive at least
a warning for the first instance and at least a loss of grade in repeated instances. If it is
a serious matter you will receive at least a zero on the relevant assignment, and if it is
a major matter you will fail the course. The words ”at least” indicate that more severe
consequences will occur if circumstances make them appropriate.
Expectations
Problem sets and other homework are typically collaborative, which means the following. You may use the notes, your book, and me without attribution. You may work with
other students in the class, you may consult other books and online resources, but these
may only be done with attribution and separately from the writing up. When working
with other students or consulting books or online resources, any work you do or notes you
take must be disposed of afterwards. When you are writing on or looking at paper that
you will turn in to me, you may have your class notes and textbook with you, but you
may not communicate with anyone about the work, or look at any written work or other
resource related to the work. Anyone you work with and any written resources you use
must be identified on the final document (you may make notes of the names of people you
work with and books and web addresses you use, and then consult these during write up).
Failure to attribute is a minor offence. Failure to do the write up alone and without outside
resources is not an issue of academic honesty and thus I will not impose consequences, but
write-ups that are so similar (or similar to outside sources) that it is clear at least one of
the participants was writing without understanding, or consulting anyone not in the class
(without prior explicit permission), is a an academic honesty issue and is a potentially
serious offense (for all participants).
Take home tests and quizzes, including opportunities to redo in class quizzes and tests,
are noncollaborative. You may use your notes, your book and any help I give you unless
I say otherwise. You may not discuss the assignment or get help from anyone else or any
other resources, you may not give help to anyone else, and if you know of people in your
class violating these rules you should tell me. Obviously you may not look at other people’s
work. Communicating with others about the assignment (both giving and receiving aid)
and using unapproved resources is major.
In-class tests and quizzes follow the same rule as take-homes, except that you are not
permitted to use notes, the book, or on-line resources without explicit permission.
In an expository writing assignment outside written/electronic resources are permitted
during the write-up with attribution. Any wording taken from such a resource of a sentence
or longer must be quoted. Consulting with other people, in or out of class separate from
the write-up is acceptable unless I say otherwise. You may also ask people to look at,
comment on, and mark up your writing with attribution, but you may not use wording
they suggest unless it is less than a sentence in length. Failure to attribute is serious, use
of other people’s full sentences is major.
The expectations for group work (final project and maybe some problem sets), where a
group of students turn a single assignment in collectively for a single grade, are the same,
except of course there are no restrictions on collaboration within the group.