EE 325: Probability and Random Processes (Spring 2013)

Instructor: Saravanan Vijayakumaran
Schedule: Slot 5, Wednesday and Friday (9:30 am - 10:55 am)
Location: LCH 11
Piazza Signup: https://piazza.com/iit_bombay/spring2013/ee325minor

Course Outline

• Probability Spaces
• Combinatorial Probability Models
• Random Variables
• Limit Theorems
• Random Processes

Grading Policy

• 10% Assignments, 20% Quizzes, 30% Midsem, 40% Endsem
• Relative grading

Slides

• Course Information
• Probability Spaces
• Why is the Probability Space a Triple?
• Properties of Probability Spaces
• Conditional Probability
• Independence
• Sampling Models
• Random Variables
• Discrete Random Variables
• Expectation of Discrete Random Variables
• Optimal Decoding of Error Correcting Codes
• Jointly Distributed Discrete Random Variables
• Continuous Random Variables
• Generating Random Variables
• Hypothesis Testing
• Parameter Estimation
• Generating Functions
• Characteristic Functions
• Convergence of Random Variables
• Random Processes
• Power Spectral Density
• Gaussian Random Processes

Assignments

• Assignment 1, Due Date: January 23, 2013
• Assignment 2, Exercises 1.4.2, 1.4.3, 1.4.7 in Grimmett/Stirzaker, Due Date: February 1, 2013
• Practice Problems from Grimmett/Stirzaker:
  1.5.1, 1.5.2, 1.5.4, 1.5.7
  1.7.1, 1.7.2, 1.7.5
  1.8.1, 1.8.2, 1.8.4, 1.8.5, 1.8.6, 1.8.7, 1.8.15, 1.8.20, 1.8.22, 1.8.24, 1.8.25
  2.1.2, 2.1.3
  2.3.3
  2.4.1, 2.4.2
  2.5.4
  2.7.1, 2.7.4, 2.7.5, 2.7.6, 2.7.7, 2.7.9
  
• Practice Problems from Grimmett/Stirzaker:
  3.1.1, 3.1.3, 3.1.4
  3.2.1, 3.2.2, 3.2.3, 3.2.4, 3.2.5
  3.3.1, 3.3.2, 3.3.3, 3.3.6, 3.3.8
  3.5.2
  3.11.1, 3.11.2, 3.11.4, 3.11.8, 3.11.13, 3.11.14, 3.11.16
  
• Assignment 3, Due Date: March 15, 2013
• Practice Problems from Grimmett/Stirzaker:
  4.1.2, 4.1.3
  4.2.1, 4.2.2, 4.2.3
  4.3.2, 4.3.3, 4.3.4, 4.3.5
  4.5.4, 4.5.8
  4.7.2, 4.7.3, 4.7.4, 4.7.10
  4.8.1
  4.11.1, 4.11.8
  4.14.4(a), 4.14.7, 4.14.14, 4.14.17
  

Exams

• Quiz 1, Date: February 8, 2013
• Midsem, Date: February 22, 2013
• Quiz 2, Date: March 20, 2013
• Quiz 3, Date: April 12, 2013
• Endsem, Date: April 29, 2013

Reference Books

• Probability and Random Processes, Geoffrey Grimmett and David Stirzaker, 2001 (Third Edition)
• Elementary Probability Theory, Kai Lai Chung and Farid AitSahlia, 2003 (Fourth Edition)
• One Thousand Exercises in Probability, Geoffrey Grimmett and David Stirzaker, 2001