MATH
4342 -- Mathematical Statistics I -- Fall 2019
Instructor
Dr. Alex
Trindade, 228 Mathematics & Statistics Building.
E-mail: alex.trindade"at"ttu.edu; Phone: 834-6164.
Course Meets: 12:30 - 13:50 TR, in Math 109.
Office Hours: TWR 2:00-3:00, or by appointment.
Text Books
- Required: Mathematical Statistics with Applications, 7th ed., by
Wackerly, Mendenhall, and Scheaffer, Duxbury Press, 2008. (6th ed. is ok.)
- Recommended: Accompanying Students' Solutions Manual to odd problems (ISBN-13:
978-0-495-38506-6).
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 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 chapters 1-2 (20%). Thursday Sep 19.
- Test 2, over chapter 3 (20%). Thursday Oct 10.
- Test 3, over chapter 4 (20%). Thursday Oct 31.
- Test 4, over chapter 5 (20%). Thursday Nov 21.
- Final Exam, comprehensive (40%): Saturday Dec 7, 1:30 p.m. to 4:00 p.m.
Test dates are fairly firm, but will be confirmed at
least one week beforehand. 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.
Suggested Homework Problems
In order to master the course material it's essential to work as many
exercises as possible. Many test questions will either be drawn from
the list of suggested homework problems below, or will be very
similar in character. The following list of exercises from the text (corresponding 6th edition problems are in parenthesis) represents the
kinds of problems you should be able to solve; do as many as
possible. Some problems may require considerable effort on
your part, but this is an important part of the learning process which
cannot be replaced with simply looking up the solutions. Working in
groups can be a very positive learning experience. It's crucial
that you keep up with the pace of the course by steadily working
through this list.
- Chapter 1: 17(15), 23(21), 25(23).
- Chapter 2
1(1), 3(3), 7(5), 15(13), 17(15), 19(17), 27(19), 29(21), 31(23), 33(25), 35(27), 37(29), 41(33), 43(35), 51(41), 53(43), 57(47), 65(51), 71(57), 73(59), 77(61), 79(63), 81(65), 85(67), 93(69), 95(71), 99(75), 101(77), 103(79), 105(81), 111(87), 113(89), 118(94), 121(97), 125(99), 133(111), 135(113), 137(115), 139(117), 141(119), 149(127), 155(131).
- Chapter 3
1(1), 3(3), 5(5), 9(7), 13(11), 19(13), 21(15),
23(17), 25(19), 33(23), 35(25), 39(27), 41(29), 43(31),
45(33), 55(39), 57(41), 63(47), 67(51), 69(53), 71(55), 73(57),
81(63), 83(65), 93(75), 95(77), 97(79), 103(85), 107(87), 113(91), 115(93), 127(101),
131(103), 133(105), 135(107), 139(111), 141(113), 145(115),
147(117), 149(119), 153(121), 155(123), 171(135), 173(137),
177(141), 179(143), 197(159), 205(165)
- Chapter 4
4.2: 11(5), 13(7), 15(9), 17(11), 19(13)
4.3: 21(15), 27(21), 29(23), 33(27)
4.4: 39(29), 41(31), 51(39), 57(45)
4.5: 59(47), 63(49), 65(51), 67(53), 69(55), 71(57), 75(61), 77(63)
4.6: 91(71), 93(73), 97(77), 103(81), 105(83), 107(85), 109(87), 111(89)
4.7: 123(91), 125(93), 127(95), 129(97)
4.9: 137(105), 139(107), 143(111), 145(113)
4.10: 147(115)
- Chapter 5
5.2: 3(3), 5(5), 9(7), 11(9), 13(11), 15(13), 17(15)
5.3: 19(17), 21(19), 23(21), 27(23), 29(25), 35(29), 37(31)
5.4: 45(39), 47(41), 53(45), 55(47), 57(49), 59(51), 61(53), 71(61)
5.6: 73(63), 77(65), 79(67), 81(69)
5.7: 89(75), 91(77), 93(79)
5.8: 103(87), 105(89), 107(91), 109(93)
5.9: 119(99), 121(101), 123(103), 125(105)
5.11: 133(113), 137(117)
- Chapter 6
6.3: 1(1), 3(3), 5(5), 9(7), 11(9), 15(11), 17(13), 19(15)
6.4: 23(19), 27(23), 29(25), 33(29)
6.5: 39(33), 41(35), 43(37), 49(43), 53(45), 55(47), 57(49), 59(51)
6.6: 35(31), 69(55), 71(57)
6.7: 73(59), 75(61), 81(65), 87(67)
Policies
- Class Attendance. Your attendance alone will not impact your grade,
but missing exams and assignments will. Whether an absence is excused or
unexcused is determined solely by me, with the exception of absences due to
religious observance and officially approved trips (see below).
- Make-up Exams: These may be granted in exceptional circumstances
if you provide me with a valid excuse (such as a note from a physician, an
obituary, etc.).
- Absence for observance of a religious holy day (TTU Operating Policy 34.19): 1. "Religious holy day" means a holy day
observed by a religion whose places of worship are exempt from property taxation under Texas Tax Code 11.20. 2. A student
who intends to observe a religious holy day should make that intention known to the instructor prior to the absence. A student
who is absent from classes for the observance of a religious holy day shall be allowed to take an examination or complete an
assignment scheduled for that day within a reasonable time after the absence. 3. A student who is excused under Section 2
may not be penalized for the absence; however, the instructor may respond appropriately if the student fails to complete the
assignment satisfactorily.
- Absence due to officially approved trips: The Texas Tech University Catalog states that the department chairpersons, directors, or others responsible for a student representing the university on officially approved trips should notify the student's instructors of the departure and return schedules in advance of the trip. The instructor so notified must not penalize the student, although the student is responsible for material missed. Students absent because of university business must be given the same privileges as other students.
- Illness and Death Notification. The Center for Campus Life is responsible for notifying the campus community of student illnesses, immediate family deaths and/or student death. Generally, in cases of student illness or immediate family deaths, the notification to the appropriate campus community members occur when a student is absent from class for four (4) consecutive days with appropriate verification. It is always the student's responsibility for missed class assignments and/or course work during their absence. The student is encouraged to contact the faculty member immediately regarding the absences and to provide verification afterwards. The notification from the Center for Campus Life does not excuse a student from class, assignments, and/or any other course requirements. The notification is provided as a courtesy.
- ADA accommodations (TTU Operating Policy 34.22). Any student who, because of a disability, may require some special
arrangements in order to meet course requirements should contact the instructor as soon as possible to make any necessary
arrangements. Students should present appropriate verification from Student Disability Services, during the instructor's office
hours. Please note instructors are not allowed to provide classroom accommodations to student until appropriate verification
from Student Disability Services has been provided. For additional information, you may contact the Student Disability
Services office at 335 West Hall or 806-742-2405.
- Civility in the Classroom. It is expected that everyone will behave
in a manner that is conducive to learning. One common disruption is cell
phones. Please turn these off in class.
- Academic Honesty (TTU Operating Policy 34.12). It is the aim of the faculty of Texas Tech University to foster a spirit of
complete honesty and high standard of integrity. The attempt of students to present as their own any work not honestly
performed is regarded by the faculty and administration as a most serious offense and renders the offenders liable to serious
consequences, possibly suspension. "Scholastic dishonesty" includes, but it not limited to, cheating, plagiarism, collusion,
falsifying academic records, misrepresenting facts, and any act designed to give unfair academic advantage to the student
(such as, but not limited to, submission of essentially the same written assignment for two courses without the prior
permission of the instructor) or the attempt to commit such an act.
- Electronic Devices in Tests. Scientific calculators 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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