# Course Information

Introduction to Random Variables and Random Processes - Spring 2010

Instructor: Prof. Songhwai Oh (오성회) Email: songhwai (at) snu.ac.kr Office: Building 301 Room 702 Phone: 880-1511 |
Course Number: 420.314 003 Time: M/W 11:00-12:30PM Location: Building 301 Room 202 |

## Course Description

This course introduces the fundamentals of probability and random processes useful in many areas of electrical engineering. The objective is to equip students with the basic tools in probability required to build and analyze probabilistic models in both discrete and continuous spaces. Topics include sample space, events, probability law, conditional probability, independence, random variables, distribution, density functions, law of large numbers, central limit theorem, random vectors, and random processes.

## Announcements

- [5/26/2010] The final exam will be held from 11am to 1pm, June 14th, Monday (Building 301 Room 202).
- [5/03/2010] The second midterm will be held in class on May 10th, Monday. The exam is closed book and closed notes and no electronics are permitted.
- [3/31/2010] The first midterm will be held in class on April 5th, Monday. The exam is closed book and closed notes and no electronics are permitted.
- [3/10/2010] The teaching assistant (TA) for this course is Mr. Yoon, SangSeok. His email address is skywalker (at) snu.ac.kr. You can also reach him by phone at 880-1512.
- [3/09/2010] The first midterm will be held on April 5th (Mon) and the second midterm will be held on May 10th (Mon).

## Reading

Week | Date | Reading | Date | Reading |
---|---|---|---|---|

1 | 3/3 | Gubner Ch. 1.1-1.2 | ||

2 | 3/8 | Gubner Ch. 1.3-1.5 | 3/10 | Gubner Ch. 1.6-1.7 |

3 | 3/15 | Gubner Ch. 2.1-2.3, Ch. 3.2 | 3/17 | Gubner Ch. 2.4 |

4 | 3/22 | Gubner Ch. 3.4-3.5 | 3/24 | Gubner Ch. 4.1-4.2 |

5 | 3/29 | Gubner Ch. 4.3-4.4 | 3/31 | Review |

6 | 4/5 | Midterm I | 4/7 | Gubner Ch. 5.1-5.2 |

7 | 4/12 | Gubner Ch. 5.2-5.5 | 4/14 | Gubner pp.87-90, Ch. 3.3, 5.6 |

8 | 4/19 | Gubner Ch. 7.1-7.3 | 4/21 | Gubner pp.91-96, Ch. 7.4-7.5 |

9 | 4/26 | Gubner Ch. 8.1-8.2 | 4/28 | Gubner Ch. 8.3-8.4 |

10 | 5/3 | Review | 5/5 | No class |

11 | 5/10 | Midterm II | 5/12 | Gubner Ch. 8.4 |

12 | 5/17 | Gubner Ch. 9.1-9.5 | 5/19 | Gubner Ch. 10.1-10.2 |

13 | 5/24 | Gubner Ch. 10.3-10.5 | 5/26 | Gubner Ch. 10.6 |

14 | 5/31 | Gubner Ch. 12.1-12.2 | 6/2 | No class |

15 | 6/7 | Gubner Ch. 12.3-12.4 | 6/9 | Review |

16 | 6/14 | Final Exam (11-1PM) |

## Textbook

**[Required]**John A. Gubner. Probability and Random Processes for Electrical and Computer Engineers. Cambridge University Press, 2006.- [Reference] Leon-Garcia, Probability and Random Processes for Electrical Engineering, Addison Wesley, 2008 (Third Edition).

## Topics

- Introduction to probability (sample space, events, and axioms of probability)
- Conditional probability, independence
- Discrete random variables
- Expectation
- Moment generating functions, weak law of large numbers
- Conditional probability
- Continuous random variables
- Cumulative distribution functions (CDFs)
- Properties of CDFs and central limit theorem
- Joint and marginal probabilities
- Random vectors
- Multivariate Gaussian distribution
- Random processes
- Stationary processes, power spectral densities
- Markov chains (if time permits)