Syllabus Spring 2000
MTH 451 - Introduction to Probability and Statistics
Mon. Wed. Fri 2:00 BLISS 211
Professor: Nancy Eaton
Office: Tyler 222
phone: 874-4439, Office Hours: Wed. 10-11, Thurs. 10-12
or by appointment
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.
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
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.
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.
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.
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.
File translated from TEX
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