MATH
4342 -- Mathematical Statistics I -- Fall 2026
Instructor
Dr. Alex
Trindade, 233 Mathematics & Statistics Building.
E-mail: alex.trindade"at"ttu.edu.
Course Meets: 14:00 - 15:20 TR, in Math 010.
Office Hours: ???, or by appointment.
Text Books
- Recommended: Mathematical Statistics with Applications, 8th ed., by
Wackerly, Chen, and Loy, Cengage Learning, 2027. (earlier eds. ok.)
- Required: WebAssign, for homework assignments (also gives access to ebook).
Course Objectives
The sequence MATH 4342-4343 develops the basic mathematical theory of
statistical inference at an undergraduate level. Three semesters of
calculus are prerequisite for
this course (MATH 2450). MATH 4342 introduces the concepts and methods of
probability and distribution theory. In MATH 4343, these tools are used
to develop the theory of statistical estimation and hypothesis
testing. MATH 4342 is a required course for minoring in Actuarial Science at TTU, and forms
the basis for the CAS/SOA Exam 1/P (Probability).
Topics to be Covered
Chapters 1-6 of the book: basics of discrete probability; discrete and
continuous random variables and their distributions; calculation of
means, variances, and other expectations; moment generating
functions; multivariate probability distributions; variances and
covariances of linear combinations of random variables; and finally
methods for finding the distributions of functions of random variables.
Course Notes
These notes are somewhat rough, but constitute a fairly complete log of what I'll be covering in class. Suggestion: bring a printed copy to class and oultine what I actually cover.
Expected Learning Outcomes
After completing this course the student should be able to:
- Calculate probabilities of events using counting rules; calculate conditional
probabilities; determine independence of events; apply the Law of Total
Probability and Bayes' Rule.
- Calculate probabilities, moments, and moment-generating functions for discrete random variables;
recognize the following standard discrete distributions: binomial, geometric,
hypergeometric, poisson.
- Calculate probabilities, moments, and moment-generating functions for continuous random variables;
recognize the following standard continuous distributions: uniform, normal, gamma, beta.
- Calculate probabilities and moments for multivariate distributions; obtain
marginal and conditional distributions; calculate covariance and correlation
and determine independence of random variables; obtain expectations and
variances for linear combinations of random variables.
- Find the distribution of a function of random variables using the methods
of: distribution functions, transformations, and moment-generating functions;
perform bivariate transformations using jacobians; calculate joint
distributions and moments of order statistics.
Methods of Assessing the Expected Learning Outcomes
The course grade will be determined
from the WebAssign hwk problems (10%), four (4) semester end-of-chapter tests, and a comprehensive final
exam. The lowest grade on tests 1, 2, and 3, will be dropped. The
tests are weighted as follows.
- Test 1, over chapter 2 (20%). Thursday Sep 17.
- Test 2, over chapter 3 (20%). Tuesday Oct 13.
- Test 3, over chapter 4 (20%). Thursday Oct 29.
- Test 4, over chapter 5 (20%). Thursday Nov 19.
- Final Exam, comprehensive (40%): ??? Dec ??, ???.
Special review session may be scheduled prior to
each test. Course averages of at least 90%, 80%, 70%, and 60% will guarantee
letter grades of A, B, C, D, respectively.
Homework Problems
These are available through WebAssign and constitute 10% of the grade. Hwk 2 covers
the material in Ch 2 and will be due on the midnight preceeding Test 2. Similarly for
Hwks 3, 4, 5, and 6. In order to master the course material it's essential to work as many
exercises as possible. It is highly recommended that you complete all hwk assignments and
additionally work the Supplementary Problems at the end of each chapter. Many test questions
will either be drawn from these, or will be very similar in character.
My Policies (TTU policies are on the Canvas page)
- Class Attendance. Your attendance alone will not impact your grade,
but missing exams and assignments will. Make-up exams may be granted in exceptional circumstances
if you provide me with a valid excuse (such as a note from a physician, an obituary, etc.).
- Electronic Devices in Tests. Scientific calculators (not laptops, tablets, or phones) are capable of performing some
of the calculations for the course. These are permitted, and are in fact necessary in some questions.
However, you should not rely on your
calculator to automatically "spit-out" answers to the more complex
questions. Most questions on tests will be of a
partial-credit type nature, and hence require you to show the steps in
obtaining the answer. If you simply write the final answer, you may only get a
small proportion of the points, even if your answer is correct. Finally, any kind of
communication-capable device (smartphones, tablets, laptops, etc.) is forbidden.
- Collaboration. My policies on this are as follows.
- Homeworks: Discussion with peers regarding material/concepts covered in the
course is permitted, and is encouraged since it usually leads to greater comprehension.
- Tests: Any form of collaboration on tests, including e-device communication or trying to see what the person next to you is writing, is strictly forbidden and will not be tolerated.
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