Paul J. Hurtado

Probability Theory (MATH 461/661)

Spring 2015 course website

Office Hours: TW 1-2pm (or by appointment) in 220 DMSC
Lectures: 9:30am-10:45am, Tues & Thurs, 20 Jan - 5 May, 2015 in SLH 3 (map)    
Final Exam: 12:30-2:30pm on Tuesday, 12 May 2015. (PDF of Spring 2015 Final Week Schedule).

Description: Probability space axioms; random variables, expectation, univariant and multivariant distribution theory, sequences of random variables, Tchebychev inequality, law of large numbers, and central limit theorem.

Syllabus: Click here to download (PDF).
(Updated 23 Jan 2015)
Course website: http://www.pauljhurtado.com/teaching/SP15/

Course Information

• Week 1 -- Lecture Notes (PDF).
  • Tues -- Introduction
  • Thurs -- Begin Ch 2. Basic definitions.
    Homework #1 (Due Thurs, 29 Jan): Click here for PDF.
    Get started typing up your homeworks in LaTeX here.
• Week 2 -- Lecture Notes (PDF).
  • Tues -- Sections 2.3-2.5
  • Thurs -- Homework #1 due.
    Homework #2 (Due Thurs, 5 Feb): Click here for PDF.
    
• Week 3 -- Lecture Notes (PDF).
  • Tues -- Sections 2.5-2.6
  • Thurs -- Sections 2.6-2.7
    Homework #3 (Due Thurs, 12 Feb): Click here for PDF.
    
• Week 4 -- Lecture Notes (PDF).
  • Tues -- Sections 3.1-3.2
  • Thurs -- Sections 3.1-3.2
    Homework #4 (Due Thurs, 19 Feb): Click here for PDF.
    
• Week 5 -- Lecture Notes (PDF).
  • Tues -- Sections 3.3-3.4
  • Thurs -- Sections 3.4-3.5
    Homework #5 (Due Thurs, 26 Feb): Click here for PDF.
    
• Week 6 -- Lecture Notes (PDF).
  • Tues -- Sections 3.5
  • Thurs -- Sections 3.5-3.6
    Homework #6 (Due March, 5 Feb): Click here for PDF.
    
• Week 7 -- Lecture Notes (PDF) See the Week 9 notes below.
  • Tues -- Sections 3.6-3.7; Motivation for Multivariate: OLS and Liklihood [PDF] [Rnw]
  • Thurs -- Sections 3.7-3.8. No Homework to prepare for exam.
• Week 8 --
  • Tues -- Sections 3.8, 3.11; Review for Exam #1
  • Thurs -- EXAM #1
    

------------ S P R I N G     B R E A K ! ------------


• Week 9 -- Lecture Notes (PDF).
  • Tues -- Sections 3.7-3.8,3.11
  • Thurs -- Sections 3.8, 3.11, 3.9
    Homework #7 (Due Thurs, 2 Apr): Click here for PDF.
    
• Week 10 -- Lecture Notes (PDF).
  • Tues -- Variance, Covariance, review Exam #1 solutions.
  • Thurs -- Finish Ch. 3 (except perhaps 3.10)
    Homework #8 (Due Thurs, 9 Apr): Click here for PDF.
    
• Week 11 -- Week 11 & 12 Lecture Notes (PDF).
  • Tues -- Special Distributions (Ch. 4 plus additional material).
  • Thurs -- GUEST LECTURE by Ania Panorska. Special Distributions (Ch. 4 plus additional material)
    Homework #9 (Due Thurs, 16 Apr): Click here for PDF.
    
• Week 12 -- Week 11 & 12 Lecture Notes (PDF).
  • Tues -- Ch 4 continued
  • Thurs -- Ch 4 continued
    Homework #10 (Due Thurs, 23 Apr): Click here for PDF.
    
• Week 13 -- Lecture Notes (PDF) and Probability Distributions Table (PDF)
  • Tues -- Finish Ch 4 (named distributions), begin Convergence concepts, Law of Large Numbers
    Probability Distributions Table (PDF)
  • Thurs -- Finish Convergence Concepts and Central Limit Theorem; Exam Review
• Week 14
  • Tues -- EXAM #2. During the exam, this Probability Distributions Table (PDF) will be provided.
    
  • Thurs -- Further Topics in Probability Theory
• Week 15
  • Tues -- Last Day of Class. MUST BE PRESENT TO OPT OUT OF THE FINAL
• FINAL EXAM
  • Tuesday, 12 May, at 12:30-2:30pm (PDF of Spring 2015 Final Week Schedule).