# Syllabus Spring 2000 MTH 451 - Introduction to Probability and Statistics  Mon. Wed. Fri 2:00 BLISS 211

## Course Content and Materials

We will use Mathematical Statistics by John E. Freund. This is an introductory course covering the basic concepts and tools used in probability and statistics. The theoretical foundation will be rigorous and requires knowlege of calculus through multivariable calculus. Topics covered are: probability spaces, combinatorial counting techniques for discrete probability spaces, conditional probability and independent events, random variables, expectations, probability distribution and density functions, moments, Special Distributions, and more. The emphasis for the course will be placed equally on theory and applications. We will apply the tools learned to various problems. You will need a scientific calculator for this course.

## Sample Problems

• Find the probability that seven of 10 persons will recover from a tropical disease if we can assume independence and the probability is 0.80 that any one of them will recover from the disease.

• The number of marriage licenses issued in a certain city during the month of June may be looked upon as a random variable with mean 124 and standard deviation 7.5. According to Chebyshev's theorem, with what probability can we assert that between 64 and 184 marriage licenses will be issued there during a month of June?

If X is the proportion of persons who will respond to one kind of mail-order solicitation, Y is the proportion of persons who will respond to another kind of mail-order solicitation, and the joint probability density of X and Y is given by

f(x,y) =  ì
í
î
 2(x+4y)/5
 for 0 < x < 1, 0 < y < 1
 0
 elsewhere
find the probabilities that
• at least 30 percent will respond to the first kind of mail-order solicitation;
• at most 50 percent will respond to the second kind of mail-order solicitation given that there has been a 20 percent response to the first kind of mail-order solicitation.

## Homework and Classroom Assignments

Fifteen percent of your grade will be based on your homework. Ten percent is based on work done in the classroom, written and at the board. Homework will be assigned regularly from problems in the book. You should expect to spend an average of 5 hours per week on your homework. Keep these well organized in a notebook. I will collect a sampling of this homework and throughout the semester I will ask each student to present some solutions to the class. During class we will have breaks from the lecture so that you may work out examples at your seats most often in groups. Sometimes I will collect this and count it toward the classwork portion of your grade. Be sure to keep up with your homework assignments and get them in by the due dates.

Find one article from a journal which illustrates an application of probability and summarize it to the class.

## Class Attendence

I don't require you to attend class, but I firmly believe that your success in this course will be greatly hindered if you do not attend class. In order to succeed on the tests, you have to know what was covered and emphasized in class. You must also attend class to find out the daily homework assignments and perform the classroom assignments. The classroom assignments are designed to help you with your understanding of the material so that when you try the problems on your own at home, you won't have as many questions.

## Office Hours

Please make use of my office hours to ask questions. You should solve every homework problem assigned. If you think you didn't get the correct answer or you don't know how to get the correct answer, ASK. Ask BEFORE you hand it in for a grade. There is a conference room in the math department that you may use to work in and meet your classmates for study groups. It is then convenient to pop over to my office for questions when I am available.

## Tests

There will be three hour long exams and a Final. The three exams are worth 45% of your grade and the final will be worth 30% of your grade. The dates for the exams are as follows: February 16, March 22, and April 17. The final, given on Tues. May 9 11:30-2:30, will be comprehensive. The exams will contain problems similar to those given in class and in your homework.

## Other essential information

You should read the book, reading thoroughly the sections that we cover, after we cover them and glancing ahead over the sections that will come next. The examples given in the text should complement those given in class. I try to give similar but different examples to those given in the book so that you have more to work from. Reading the book will clarify those points given in class and reading ahead will help to prepare you for what is coming next so that what is said in class will be better understood.

I recommend that you get some index cards and use them for studying. After each class you can summarize the lesson by writing down the important points on index cards. Then the information is handy for when you are working on homework.

On each card write down a single definition or theorem or important example. When you study for tests, you can glance through the cards to make sure you understand each of these ideas. If you don't remember one clearly you can then go and look it up and do some examples. Also, while I'm presenting something new in class, I will expect you to know and understand all of the previous material. You might need to quickly look up a definition that you don't remember, while I'm talking. The cards may come in handy in such an instance. Through constant use ofhese cards, you will naturally memorize the material well in advance of taking the tests. I would expect that you would be familiar with what is on the cards through continuous use while doing homework problems and seeing it in class.

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