Holy Cross Mathematics and Computer Science
Mathematics 376 -- Probability and Statistics II
Syllabus Spring 2004
Professor: John Little
Office: Swords 335
Office Phone: 793-2274
Office Hours: MW 10 - 12, TR 1 - 3, F 8 - 9, and by appointment
Email: little@mathcs.holycross.edu (prefered), or jlittle@holycross.edu
Course Homepage: http://mathcs.holycross.edu/~little/ProbStat/PS2.html
Course Description
Statistics is the branch of the mathematical sciences
that deals with quantities that vary in more or less unpredictable
or random ways, and with the collection, analysis, and
interpretation of data concerning those quantities. It is used
very widely today in the physical, life, social, and management
sciences for making decisions and predictions in the presence of
uncertainty. Some typical examples are:
- Demonstrating evidence for an empirical relationship
between different quantities in a physics experiment, where measurement
errors or fundamental elements of randomness (e.g. quantum physical
effects) may be present,
- Analyzing the results of treating patients with a new drug
in a clinical trial, where the reaction of an individual patient
depends on too many different types of factors to be predictable,
- Predicting the outcome of an election by sampling voter preferences
(see below for a fuller discussion of this case),
- Estimating how to price an insurance policy based on likely
risks to the persons covered. (This is a large part of what
actuaries do in insurance companies; Probability and
Statistics is the subject of one of the first in the series of
exams actuarial trainees must pass to become qualified.)
Indeed statistical reasoning is probably the most common use
of mathematics in real world applications at present.
This course is a continuation of Probability and Statistics I from
the fall semester. This term, we will apply almost all of the
concepts from probability that we learned last fall to study
statistical inference procedures for estimating parameters
describing the distributions of characteristics in a population
(e.g mean, standard deviation, fraction possessing the characteristic,
and so forth), or for identifying models describing the population.
The course will be organized as follows:
- Unit I: Sampling Distributions and the Central Limit Theorem --
The Theoretical Basis of Statistics (Chapter 7 of WMS, about 7 class days)
- Unit II: Estimating Population Parameters -- Point Estimators,
Interval Estimators and Confidence
Intervals, and Selecting Sample Sizes (Chapter 8 of WMS, about 8 class days)
- Unit III: Properties of Estimators -- efficiency, consistency,
sufficiency; Deriving Estimators -- Method of Moments and Method
of Maximum Likelihood (Chapter 9 of WMS, about 6 class days)
- Unit IV: Hypothesis Testing -- The Design and Rationale of
Statistical Tests (Chapter 10 of WMS, about 9 class days)
- Unit V: Linear Models and Regression for Parameter Estimation
(Chapter 11 of WMS, about 8 class days)
The remaining 2 class days will be devoted to 2 in-class midterm exams
(see below for dates).
A more detailed day-by-day schedule will be maintained on the
course homepage for you to consult as needed.
Text
The text for this semesters of the course is the same as last term:
Mathematical Statistics with Applications, 6th ed
by D. Wackerly, W. Mendenhall, and R. Scheaffer. We will
cover most of the material in Chapters 7-11 this semester,
with occasional detours back to Chapter 6 as needed.
Course Assignments and Grading
The assignments for the course will consist of:
- Two in-class midterm exams, together worth 35% of
the course grade. Tentative dates:
Friday, February 27 and Friday, April 16. If the
class agrees, these may be given at an evening time
to remove the element of time pressure. If that option
is taken, the Friday class meetings those weeks will
be cancelled.
- Final examination, worth
30% of the course grade. (Scheduled date:
Wednesday, May 12 at 2:30pm.)
- Weekly problem sets, worth 25% of the course
grade. Notes:
- I will put complete solutions of all assigned
problems on reserve in the Science Library after class on the date
the assignment is due. You may consult these and photocopy them
for your own use at any time if you wish.
- Because of the availability of these complete solutions,
because every effort will be made to return your graded problem
sets in a timely fashion, and for reasons of fairness,
no problem sets will be accepted for credit after the announced due date,
except in the case of a verified medical excuse. If you
are authorized to hand in a problem set late, I will ask you
sign a statement that you have not consulted the reserve
solutions in preparing your work.
- Group Computer Lab Projects -- Four days during the
semester we will meet in the HA 408 PC Lab to work in small groups
on computer lab projects. Each project will lead to a writeup,
together worth 10% of the course grade.
If you ever have a question about the grading policy, or about your
standing in the course, please feel free to consult with me.
Departmental Statement on Academic Integrity
Why is academic integrity important?
All education is a cooperative enterprise between teachers and
students. This cooperation works well only when there is trust and
mutual respect between everyone involved.
One of our main aims as a department is to help students become
knowledgeable and sophisticated learners, able to think and work
both independently and in concert with their peers. Representing another
person's work as your own in any form (plagiarism or ``cheating''),
and providing or receiving unauthorized assistance on assignments (collusion)
are lapses of academic integrity because they subvert the learning process
and show a fundamental lack of respect for the educational enterprise.
How does this apply to our courses?
You will encounter a variety of types of assignments and examination
formats in mathematics and computer science courses. For instance,
many problem sets in mathematics classes and laboratory assignments
in computer science courses are individual assignments.
While some faculty members
may allow or even encourage discussion among
students during work on problem sets, it is the expectation that the
solutions submitted by each student will be that student's own work,
written up in that student's own words. When consultation with other
students or sources other than the textbook occurs, students should
identify their co-workers, and/or cite their sources as they would for
other writing assignments. Some courses also make use of collaborative
assignments; part of the evaluation in that case may be a rating of each
individual's contribution to the group effort.
Some advanced classes may use take-home
examinations, in which case the ground rules will usually allow no
collaboration or consultation.
In many computer science classes, programming projects are
strictly individual assignments; the ground rules
do not allow any collaboration or consultation here either.
What are the responsibilities of faculty?
It is the responsibility of faculty in the department to
lay out the guidelines to be followed for specific assignments in
their classes as clearly and fully as possible, and to
offer clarification and advice concerning those guidelines
as needed as students work on those assignments.
The Department of Mathematics and Computer Science upholds the
College's policy on academic honesty.
We advise all students taking mathematics or computer science courses
to read the statement in the current College catalog carefully and
to familiarize themselves with the procedures which may be
applied when infractions are determined to have occurred.
What are the responsibilities of students?
A student's main responsibility is to follow the guidelines laid down
by the instructor of the course. If there is some point about the
expectations for an assignment that is not clear, the student is responsible
for seeking clarification. If such clarification is not immediately available,
students should err on the side of caution and follow the strictest possible
interpretation of the guidelines they have been given.
It is also a student's responsibility to protect his/her
own work to prevent unauthorized use of exam papers, problem solutions,
computer accounts and files, scratch paper, and any other materials used in
carrying out an assignment. We expect students to have the integrity to say
``no'' to requests for assistance from other students when offering that
assistance would violate the guidelines for an assignment.
Specific Guidelines for this Course
Because of the large size of this class, examinations will be given
in class, and the other assignments will be weekly individual problem
sets. Some examinations may be given as open book and/or open notes
tests. No sharing of information of any form with other students will
be permitted during exams. On the problem sets, discussion of the
questions with other students in the class, and with me during office
hours is allowed, even encouraged. Consultation of other probability and
statistics texts in the library for ideas leading to a problem solution
will also be allowed. If you do take advantage of any of these
options, you will be required to state that fact in a "footnote"
accompanying the problem solution. Failure to follow this rule
will be treated as a violation of the College's Academic
Integrity policy.