MAT3240 - Probability Theory, Fall
Instructor: Dr. Christopher Aubuchon
Office Hours: It's complicated. Check my office door for my schedule. It will be there before the end of our first week.
Time and Place: Monday and Wednesday from 10:00 a.m. to 11:15 a.m. in Dewey 131.
Text: INTRODUCTION TO PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS, by Walter Rosenkrantz.
Content and Objectives for this Course: Hopefully we will cover Chapters 2 through 5, and some of Chapter 6 if time permits. Check the table of contents for an outline of the content included in these chapters. In this class we will attempt to:
· To apply the mathematical ideas learned in previous mathematics courses, such as calculus, to topics in probability theory and statistics.
· To learn how to apply axioms and theorems to more complex mathematical ideas.
· To learn the technique for solving probability problems involving both discrete and continuous probability theory.
· To understand the most commonly encountered discrete and continuous random variables (i.e. to know their distribution functions, and probability density functions for a global overview of the random variables’ behavior: to know what their expected values, variances, and moment-generating functions are; and to study their applications to real phenomena).
We may even attempt :
· To emphasize the aspects of probability theory that are needed to use probability models in applications to real situations, particularly in statistics and stochastic modeling.
· To develop an understanding of the interrelationship between probability theory, mathematical statistics, and data analysis.
An Assumption of Mine: I assume that you are (basically) competent in the topics of MAT2030: Probability and Statistics, with a solid background in the topics of integral calculus. I assume also that you are self-motivated, and that you will seek assistance outside of class if your performance is at less than a "C" level.
Technical Notes: A TI-83 (or TI-84) graphing calculator is required for this course, and we will be using it quite frequently. Blah-blah-blah; I know you already have one... Hopefully we can make the calculator do some things that we wouldn’t want to do by hand ourselves. Maybe cook a burrito.
Homework: Each day I will assign numerous exercises for your practice, and enjoyment. Typically I will select most (quite often all) of these for grading. Naturally, I won’t tell you which ones will be graded because I want you to do them all! Each assignment receives a grade of 0 to 10 points, based upon accuracy and completeness. Skipping just one problem virtually guarantees that you will not receive the full 10 points for that assignment. At the end of the semester, if I have ten such grades, I can add these together to get a homework grade between 0 and 100 for you. Homework will generally be collected on Wednesdays and returned on Mondays. (Yes, I'm collecting and grading homework.)
Quizzes: There will be no weekly quizzes in this course. Fancy that!
Exams: There will be 3 midterm exams (100 points each) and a single comprehensive final exam (100 points). The final exam will be virtually impossible but, please try your best. You must attend the final at its scheduled time (found in the JSC course bulletin). Otherwise you will receive a grade of 0 for it.
Makeups: (Pay careful attention here) It is infeasible for me to accommodate students with different times/places for the administration of exams, regardless of the reason. So there will be no makeups. Attend every class on time to make sure that you do not miss anything. Should you ever miss an exam, I may allow your final exam to count for a larger percentage to make up the difference, depending upon the circumstances. Here's a tip: If ever you miss an exam or assignment, and you want me to know why, don't wait until the next class period (when you happen to see me again) to fill me in - doing so will nullify your chances of receiving any special consideration. Notify me immediately. I have a phone, and an email address, and a door to pin notes to... - use them if necessary.
Grading: Your final grade will (basically) be a weighted average of your homework grade (20 %), midterm exams (60 % total), and final exam (20 %). Your weighted average will of course fall between 0 and 100. The normal scale of A = 90 – 100, B = 80 – 89, C = 70 – 79, etc… will be used.
Note: Absences and late arrival to class pose a problem in this course. I usually don't question the reason, but I have decided to allow all students THREE excused absences/late arrivals. You can claim then whenever you wish; use them wisely. All other absences or late arrivals are considered UNEXCUSED and will result in a 1 point deduction on your final average. Seriously.
final note: Attend
class, be on time, do all your work on time, and pay attention.
This way we can all gain a better understanding of probability theory and its
applications. I am hoping that some of our meetings can become informal
discussions about the subject matter. We’ll see. If you need any help be sure to
contact me. Good luck!
GOOD LUCK !
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Lecture Notes and Class Notes for Probability Theory, organized (roughly) by section
(To accompany Introduction to Probability and Statistics for Scientists and Engineers, by Walter Rosenkrantz)
|Week One||Monday, August 27||Class canceled due to Opening Convocation|
|Wednesday, August 29||Some Set Theory|
|Week Two||Monday, September 3||Axioms of Probability Theory|
|Wednesday, September 5||Continuation of above.|
|Week Three||Monday, September 10||Combinatorial Analysis|
|Wednesday, September 12||Continuation of above.|
|Week Four||Monday, September 17||Conditional Probability|
|Wednesday, September 19||Baye's Theorem.|
|Week Five||Monday, September 24||Class canceled.|
|Wednesday, September 26||Review of homework exercises.|
|Week Six||Monday, October 1||Random Variables|
|Wednesday, October 3||Exam One (Chapter 2)|
|October 8-12||FALL BREAK||Relax and enjoy!|
|Week Seven||Monday, October 15||Expected Value|
|Wednesday, October 17||Geometric Distribution|
|Week Eight||Monday, October 22||More discussion of expected value.|
|Wednesday, October 24||Hypergeometric Distribution|
|Week Nine||Monday, October 29||The Binomial Distribution|
|Wednesday, October 31||Continuation of above.|
|Week Ten||Monday, November 5||Chebyshev's Theorem|
|Wednesday, November 7||Review for Exam Two.|
|Week Eleven||Monday, November 12||Continuous Random Variables|
|Wednesday, November 14||Exam Two (Chapter 3)|
|November 19-23||THANKSGIVING RECESS||And we are thankful for probability theory...|
|Week Twelve||Monday, November 26||Continuous Random Variables|
|Wednesday, November 28||Expected Value|
|Week Thirteen||Monday, December 3||Uniform and Exponential Distributions|
|Wednesday, December 5||Continuation of above.|
|Week Fourteen||Monday, December 10||The Normal Distribution|
|Wednesday, December 12||The big finish!!|
|FINAL EXAM||Wednesday, December 19, 8:00 a.m.|
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Homework for Probability Theory
|Assignment||Date Assigned||Date Due|
|Set-theoretic Diversion (worksheet)||August 29||September 5|
|2.1, 2.2, 2.3||September 3||September 5|
|2.4 through 2.13||September 5||September 12|
|2.14, 2.15, 2.17, 2.18||September 10||September 12|
|2.19 through 2.29||September 10||September 19|
|2.30 through 2.40||September 17||September 26|
|From 2.41 through 2.44, choose exactly 3 problems||September 19||September 26|
|3.1 through 3.12||October 1||October 17|
|3.13 through 3.25||October 22||October 29|
|3.29(a), 3.30 through 3.36, 3.41 through 3.46, 3.51||October 24||November 7|
|3.38, 3.47 through 3.49||November 5||Not to be collected.|
|4.1 through 4.12||December 3||December 10|
|4.22, 4.24-4.30||December 5||Not to be collected.|
|4.32, 4.33||December 12||Not to be collected.|
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Secondary Education Endorsement Competencies: The following is provided for students who are pursuing secondary education licensure in addition to a math major.
5440-11 Mathematics Knowledge Standards:
Demonstrates knowledge of mathematical content, concepts, and skills delineated in current national professional standards 1 and in Vermont’s Framework of Standards and Learning
SEM K1 National Council of Teachers of Mathematics (NCTM) process skills as vehicles for acquiring and using mathematics content knowledge
SEM K5 Functions
c. How to use functions to solve problems in calculus, linear algebra, geometry, statistics, and discrete mathematics
SEM K6 Data
Analysis, Statistics, and Probability
b. Use of both theory and simulation to study probability distributions, and applications of both theory and simulation in models of real phenomena;
c. Conditional probability and independence, and calculation of probabilities associated with these concepts;
SEM K7 Discrete Mathematics and Computer Science
b. Enumerative combinatorics
Some Documents to Accompany This Course
Important TI-83 Calculator Information
Sample Space for the Throwing of Two Dice
Proof of P(X = x0) = 0 for a Continuous Random Variable X
Proof that V(Z) = 1 if Z is the Standard Normal Random Variable
Proof of the Transformation of the Standard Normal Random Variable
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