## Statistics I: Probability Theory & Statistical Inference (505)

The objectives of the course are to introduce the underlying concepts of probability
and statistical inference.In particular, this course will provide a foundation in
the underlying probability theory and distribution theory required for application
of statistical inference. This theory will be built upon in STAT06 and other later
courses. It is expected that students will have a solid prerequisite foundation calculus
before enrolling in this course.

**Topics:** We will cover exploratory data analysis, probability theory, conditionalprobability,
independence, Bayes' theorem, discrete distributions (binomial, hypergeometric, geometric,
negative binomial, Poisson), moment generating functions, continuous distributions
(uniform, exponential, gamma, normal), mixed distributions, bivariate and multivariate
distributions. In addition, we will cover sampling distribution theory, correlation,
linear functions of random variables and introduce the Central Limit Theorem.

### Tentative Schedule of Weekly Topics

- Basic Concepts, Numerical Characteristics, Probability Set Functions
- Properties of Probability, Methods of Enumeration
- Random Variables, Probability Density Functions
- Distribution Functions, Mathematical Expectation
- Special Mathematical Expectations, Chebyshev's Inequality
- Correlation, Correlation Coefficient, Stochastic Independence
- Discrete Random Variables: binomial, multinomial, and Poisson distributions
- Continuous Random Variables: Gamma, Chi-Square, and Beta distributions
- Continuous Random Variables: Normal and Bivariate Normal distributions
- Sampling Theory, Transformations of Random Variables
- The t and F distributions, Order Statistics,
- Moment Generating Function Technique, distribution of the sample mean and variance
- Limiting Distributions, Stochastic Convergence
- Limiting Moment Generating Functions
- Central Limit Theorem

### Example Syllabus

#### STAT 505 Section 1- Statistics I -Probability Theory & Statistical Inference

**Instructor:** Scott Mcclintock

**Office:** Anderson 328

**Email Address:** smcclintoc@wcupa.edu

**Office Telephone:** 610-436-2893

**Office Hours:** M 3:30-5:30 MWF 10-11

**Class Time:** Mon 5:45 - 8:30

**Campus Emergencies**

For campus emergencies call WCU’s Department of Public Safety at (610)436-3311

Required Materials

Wackerly, Dennis, D., Mendenhall III, W., and Scheaffer, R.S. (2002). Mathematical
Statistics with Applications, 7th ed. Pacific Grove, CA: Duxbury Press.

**Goals **

The purpose of this course is to give you an introduction to probability theory and
probability distributions. The material presented will not only serve as a basis for
the following course (STAT 506), Mathematical Statistics II, but is extremely useful
and fascinating on its own. The course has a prerequisite of the equivalent of a standard
two-semester course in calculus, and a strong familiarity with concepts such as differentiation,
integration, infinite series, sequences, and related facts, is necessary.

We will cover Chapters 2-7 in Wackerly et al. In particular, we will explore the axiomatic approach to probability, various counting techniques, Bayes theorem, and other probability laws, random variables, probability distributions for both discrete and continuous random variables, expectations, moment generating functions, joint and conditional distributions for n random variables, measures of association (covariance and correlations), distributions of functions of random variables, order statistics, sampling distributions and the Central Limit theorem. We will focus on both theory and application in this course. You will be expected to derive theoretical results using algebra and calculus, and apply these results to real-life problems.

**Exam Schedule **We will have two in-class midterm examinations and one take home exam. The first midterm
will be 1st week in October (last half of class). The second midterm will be the first
week in November (last half of class). The take-home will be before Thanksgiving.
A cumulative final exam will be during finals week. Date and Time to be announced
in class. Attendance at examinations is crucial. Absence will be only due to legitimate
excuses. It will be the student's responsibility to coordinate with the instructor
a make-up time prior to the next class. Allowable materials for the test will be announced.
At this point, all tests are closed notes, closed books, and closed calculators.

Homework Assignments** **There will be approximately 9-10 homework assignments during the semester. Homework
should be written up neatly, organized, and stapled. The homework assignments are
an important component of the course. All problems assigned should be done as complete
as possible. Solutions will be available for most homework assignments. Each homework
group will count towards your final grade. Homework must be turned in at the due date.
Late homework with a legitimate excuse must be turned prior to the next class from
the due date. Any late homework will receive at most 75% credit.

Final Grade** **Your course grade will be determined by your performance on homework (20%), midterm
examinations (20% each), and the final exam (20%). Final course grades will be assigned
on the standard grading system.

No Class for WCU Fall Break

**DISABILITIES **We at West Chester University wish to make accommodations for persons with disabilities.
Please make your needs known by contacting me and/or the Office of Services for Students
with Disabilities at ext. 3217. Sufficient notice is needed in order to make the accommodations
possible. The University desires to comply with the ADA of 1990.

**Final Comments** -

*Attendance is not required but expected. If you need to be absent, please let me know.

*Ask questions, ask questions, ask questions!