SPRING 2019 - Probability and Measure (STAT 706) - Course Website

Office Hours: Mon/Wed 2:30-3:30pm, or by appointment
Lectures: Tues/Thurs 3:00-4:15pm, *PE 107*

Syllabus: Click here to download (PDF)

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Announcements: Final Exam is now posted on Canvas, due Wed May 15.

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Course Information

• Week 1: Jan 22, 24
  
  • Introduction, Probability measures (R Sec 1, 2; B Sec 1, 2): Lec 1, Lec 2
    Homework 1 - due Thursday Jan 31
    
  
  
• Week 2: Jan 29, 31
  
  • Existence and extension (R Sec 2; B Sec 3): Lec 3, Lec 4
    Homework 2 - due Thursday Feb 7
    
  
  
• Week 3: Feb 5, 7
  
  • Random variables, independence (R Sec 3; B Sections 4, 5): Lec 5, Lec 6
    Homework 3 - due Thursday Feb 14
    
  
  
• Week 4: Feb 12, 14
  
  • Limit sets, Borel-Cantelli lemmas, expected value of simple random variables (R Sections 3, 4; B Section 4): Lec 7, Lec 8
    Homework 4 - due Tuesday Feb 26
    
  
  
• Week 5: Feb 19, 21
  
  • Expected values of general random variables, inequalities and convergence (R Sections 4, 5; B Sections 5, 21): Lec 9, Lec 10
    General Info for Exam 1
    
  
  
• Week 6: Feb 26, 28
  
  • Laws of large numbers (R Section 5; B Sections 6, 22): Lec 11
    
  • EXAM 1 - Thursday Feb 28
    
  
  
• Week 7: Mar 5, 7
  
  • Laws of large numbers continued, distributions of random variables (R Section 5-6; B Sections 6, 22, 14, 20): Lec 12, Lec 13
    Homework 5 - due Tuesday Mar 12
    
  
  
• Week 8: Mar 12, 14
  
  • Stochastic processes, Gambler's ruin (R Section 7; B Sections 23, 7): Lec 14, Lec 15
    Homework 6 - due *Thursday* Mar 28
    
  
  
• SPRING BREAK
  
  
• Week 9: Mar 26, 28
  
  • Discrete Markov chains (R and B Section 8): Lec 16, Lec 17
    Homework 7 - due *Tuesday* Apr 9
    
  
  
• Week 10: Apr 2, 4
  
  • MCs continued, limit theorems (R and B Sections 8, 9): Lec 18, Lec 19
    Homework 8 - due Thursday Apr 18
    
  
  
• Week 11: Apr 9, 11
  
  • Large Deviations, weak convergence (R Sections 9, 10; B Sections 9, 25): Lec 20, Lec 21
    General Info for Exam 2
    
  
  
• Week 12: Apr 16, 18
  
  • Characteristic functions (R Section 11; B Section 26): Lec 22
    
  • EXAM 2 - Thursday Apr 18
  
  
• Week 13: Apr 23, 25
  
  • Central limit theorem, decomposition of probability laws (R Section 11; B Sections 27-30): Lec 23, Lec 24
    Homework 9 - due Tuesday May 7
    
  
  
• Week 14: Apr 30, May 2
  
  • Conditional probability and expectation, Martingales (R Sections 13-14; B Sections 32-35): Lec 25, Lec 26
    
  
  
• Week 15: May 7
  
  • Martingales (R Section 14; B Section 35): Lec 27
    
  • TAKE-HOME FINAL - posted on Canvas, due Wednesday May 15 at 5 PM
    
  
  

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