Spring 2007

Instructor: L. Pakula, Tyler 201, X4519, pakula@math.uri.edu, Office Hours: TTh 10-12 or by appointment

Prerequisite: MTH 243 (Multivariable Calculus) or equivalent

Text: Larsen and Marx,  Mathematical Statistics , 4th Edition, and handouts

Time: TTh 12:30-1:45

Room: Kelley 103

FINAL EXAM WILL BE ON MAY 10, 8 AM, Kelley 103

Final exam study guide. NOTE: Final will cover the whole semester's material. Study guide only has detail for material after Exam 2. Calculators will be permitted, but all calculus calculations must be shown in detail.

Exam 2 study guide
Solutions to some of the problems in 3.12, 4.2 and 4.3 are posted on the homework and notes page. I will be available in my office for questions next week as follows:
Tuesday 5/8, 10:30-12:30, 2-3
Wed 5/9, 10:30-12:30

Evaluation: Your grade will be based on quizzes, hand-in assignments, two in-class exams, and a final. There will be a quiz every week in which there is no exam. The quizzes will be based on the regular homework which will not be collected. (Special assignments, which might include use of Maple, will be collected.) Quizzes cannot be made up, but a number of lowest quiz grades will be dropped. Makeup exams will be given only for serious illness or emergency, and these must be documented. No electronic devices of any kind will be permitted on exams.

Quizzes & Assignments 25%
Two in-class exams 40%
Final 35%

Notes and selected hw solutions

Maple worksheet on discrete pdf and cdf (includes hw assignment) (CORRECTED)

Advice: Do the homework--you can't learn this subject without attempting the problems. In fact, challenging and varied problems are an essential part of the course. Review concepts and methods from calculus as needed. Find a study partner. Come to class.

What this course is about: MTH 451 is an introduction to the mathematical theory of probability using calculus. Probability theory has a tremendous variety of applications in all the sciences, including the social sciences, and in business and economics, and provides the mathematical foundation for statistics. It uses a wide variety of mathematical techniques and concepts, especially elementary set theory and combinatorics, and calculus. A main goal of this course is that you will be able to read more advanced material on probability and its applications and go on to courses in mathematical statistics and stochastic processes.

Review and application of calculus concepts : An explicit learning goal of this course is to strengthen your facility with calculus, including integration techniques, multiple integrals, the fundamental theorem of calculus, and series. You should be prepared to consult your old calculus textbook when needed. You are encouraged to use Maple or something equivalent for homework problems as a way to check your calculus computations. However, calculators capable of symbolic manipulation i.e. TI-89, will NOT be permitted on exams. Moreover, some exam questions will be specifically designed to test your skill in using and applying calculus ideas and methods.

Special audiences: If you are interested in taking the actuarial exams, this course is absolutely fundamental. We will discuss problems similar to problems on the actuarial exams during the course. For information about careers in actuarial science see Careers in actuarial science.

If you are a secondary math education major, you will most likely need to take the Praxis content exam, which contains material on discrete mathematics and probability for which this course is great preparation.

If you are an engineering, science, economics or business major, probability will be a basic part of your mathematical toolkit.

Finally, probability theory is a fundamental discipline in mathematics itself and well as the foundation for all of statistics. It can be entertaining, enlightening and sometimes surprising.

Text Readings and Problems: Specific assignments will be given in class.

Reading Problems
Chap. 1  
2.2 Sample spaces 1,2,3,8,12,13,16,17,18,20,28,29,31,32,33
2.3 Probability 2,3,4,6,9,10,13,16,
2.4 Conditional probability 1,2,3,4,6,12,13,15,21,22,26,28,29,30,40,42,43,44,48,53
2.5 Independence 1,2,4,5,14,16,19,20,22,25
2.6 Combinatorics 1,3,4,5,6,8,12,17,20,22,23,27,34,35,41,53,54
2.7 Combinatorial probability 1,2,3,4,7,10,11,13,17,18
3.2 Binomial and hypergeometric prob. 1,2,5,7,8,9,10,15,20,22,23,24,25
3.3 Discrete random variables 1,3,5,7,9,11,13
3.4 Continuous r.v.s 1,2,3,4,6,7,8,10,13,15
3.5 Expected value 1,3,4,9,12,13,14,15,22,23,27,31
3.6 Variance 2,4,5,8,10,14,15,16
3.7 Joint densities 5,7,11,13,19bce,22,39,42,43,51,52
3.8 Combining r.v.s no problems
3.9 Properties of mean and variance 3,5,6,8,11,14,16,17
Handout on Law of Large Numbers Problems in handout
3.10 Order statistics
3.11 Conditional densities 3,4,11,12,13,15,17
3.12 Moment generating functions 1,4,5,7,15,19,21
4.2 Poisson distribution 1,3,6,7
4.3 Normal dist. and Central Limit Theorem 1,2,3,5,9,10,16,17,24
4.4 Geometric distribution