STA 473c - Introduction to Mathematical Statistics I

Prerequisites::   A grade of C or better in MAT 137 Calculus II.   While not a formal corequisite, MAT 238 Calculus III is also recommended.

Catalog Description:   Elementary combinatorial probability theory, random variables, probability distributions, and moments.

Goals:   STA 473c has two overarching goals: to introduce and develop the field of probability (the area of mathematics devoted to the study of randomness); and (thereby) to lay the foundation for the study of statistical inference (the mathematical methods involved in using a sample to draw conclusions about an underlying population) in STA 474c.

Objectives:   Upon successful completion of this course you will be able to:

1. Recognize certain important probability models.
2. Use the language and techniques of mathematics to solve probability problems.
3. Continue the mathematical study of probability and statistics in STA 474c.

Course Content

1. Probability Models
A. Elementary and combinatorial methods
B. Discrete and continuous probability spaces
C. Conditional probability and independence
2. Random Variables
A. Probability density functions
B. Cumulative, conditional, and multivariate distributions
C. Independent random variables
D. Functions of random variables
E. Expectation and moments
F. Moment generating functions
G. Limit theorems
3. Families of Distributions
A. Discrete distributions (e.g., binomial, geometric, Poisson)
B. Continuous distributions (e.g., normal, gamma, beta, exponential)

Homework assignments	20%
Three "mid-term" examinations	20% each
Comprehensive final examination	20%

Grade Policy:   Grade cutoffs will be no higher than:   A greater than or equal to 90%; B 80-89%; C 70-79%; D 50-69%; F less than 50%.
Examination Dates:   Exams are (tentatively) scheduled for Monday September 27^th, Wednesday October 27^th, and Friday December 3^rd.
Final Examination:   The final examination will be given at the time scheduled by the University: Monday, December 13^th, 10:00am-noon.