Probability Theory and Mathematical Statistics 1
Axioms of probability; combinatorics; random variables, densities and distributions; expectation; independence; joint distributions; conditional probability; inequalities; derived random variables; generating functions; limit theorems; convergence results.
STAT
641
 Hours 3.0 Credit, 3.0 Lecture, 0.0 Lab Prerequisites Departmental consent. Taught Fall
Course Outcomes:

STAT 641

Upon successful completion of the course, the student will be able to:

Apply Fundamentals

Apply fundamentals of set theory and basic set operations

Enumerate the Elements

Enumerate the elements of a discrete sample space

Solve Problems

Solve problems using axioms of probability, conditional probability, independence, and Bayes theorem

Describe the Properties

Describe the properties of the named distributions

Manipulate the PDF and CDF

Manipulate the pdf and cdf of univariate and multivariate discrete and continuous random variables to calculate probabilities and find joint and conditional distributions

Find Moments

Find moments and moment generalized functions

Derive Distributions

Derive distributions for transformed random variables and order statistics

Use Inequalities

Use inequalities to create bounds on probabilities and expected values

Verify Convergence

Verify convergence in probabilty, distribution, and mean square

Prove the Central Limit Theorem

Prove the Central Limit Theorem (iid and non-identical finite variance versions) and demonstrate it by simulation