STAT 641
Download as PDF
Probability Theory and Mathematical Statistics 1
Course Description
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.
When Taught
Fall
Min
3
Fixed/Max
3
Fixed
3
Fixed
0
Other Prerequisites
Departmental consent
Title
Derive Distributions
Learning Outcome
Derive distributions for transformed random variables and order statistics
Title
Manipulate the PDF and CDF
Learning Outcome
Manipulate the pdf and cdf of univariate and multivariate discrete and continuous random variables to calculate probabilities and find joint and conditional distributions
Title
STAT 641
Learning Outcome
Upon successful completion of the course, the student will be able to:
Title
Prove the Central Limit Theorem
Learning Outcome
Prove the Central Limit Theorem (iid and non-identical finite variance versions) and demonstrate it by simulation
Title
Find Moments
Learning Outcome
Find moments and moment generalized functions
Title
Solve Problems
Learning Outcome
Solve problems using axioms of probability, conditional probability, independence, and Bayes theorem
Title
Apply Fundamentals
Learning Outcome
Apply fundamentals of set theory and basic set operations
Title
Use Inequalities
Learning Outcome
Use inequalities to create bounds on probabilities and expected values
Title
Describe the Properties
Learning Outcome
Describe the properties of the named distributions
Title
Enumerate the Elements
Learning Outcome
Enumerate the elements of a discrete sample space
Title
Verify Convergence
Learning Outcome
Verify convergence in probabilty, distribution, and mean square
