Introduction to Probability

Fall 2007
 Tuesdays, 2:10 ~4:00 PM
Fridays, 1:10 ~3:00 PM
Instructor: Dr. Berlin Chen (陳柏琳)

Tentative Topic List:

09/21

 　

Course Overview & Introduction

 　
09/28 　 Chapter 1: Sets and Probabilistic Models 　
10/02 　 Chapter 1: Conditional Probability, Total Probability Theorem and Bayes' Rule 　
10/05 　 Chapter 1: Conditional Probability, Total Probability Theorem and Bayes' Rule 　
10/09 　 Chapter 1: Independence & Counting HW-1 (Due 10/16)
10/12 　 Chapter 1: Independence & Counting 　
10/16 　 Chapter 2: Discrete Random Variables: Basics 　
10/19 　 Quiz 1 (1:10~2:10 p.m.) Scope: Sections 1.1 to 1.5
10/23 　 Chapter 2: Discrete Random Variables: Expectation, Mean, Variance HW-2 (Due 11/2)
Problem (chapter 1) 28, 36
Problems (chapter 2) 3, 4, 11
10/26 　 Discussions on  HW-1 & Quiz 1 　
10/30 　 Chapter 2: Discrete Random Variables: Basics 　
11/02 　 Chapter 2: Discrete Random Variables: Joint PMFs, Conditioning and Independence 　
11/05 　 Chapter 2: Discrete Random Variables: Joint PMFs, Conditioning and Independence 　
11/09 　 Quiz 2 (1:10~2:10 p.m.) Scope: Sections 2.1 to 2.6
11/12 　 Chapter 3: Continuous Random Variables: Basics 　
11/16 　 Midterm (12:30~2:30 p.m.) 　
11/20 　 Chapter 3: Continuous Random Variables: Basics 　
11/23 　 Chapter 3: Continuous Random Variables: Basics 　
11/27 　 Chapter 3: Continuous Random Variables: Conditioning, Expectation and Independence 　
11/30 　 School Sports Day 　
12/4 　 Chapter 3: Continuous Random Variables: Conditioning, Expectation and Independence Notice of Possible Failure to Pass
HW-3 (Due 12/11)
Problem (chapter 3) 2, 4, 7, 10
12/7 　 Chapter 3: Continuous Random Variables: Derived Functions 　
12/11 　 Quiz 3 (2:10~4:00 p.m.) Scope: Sections 3.1 to 3.5
12/14 　 Chapter 3: Continuous Random Variables: Derived Functions 　
12/18 　 Chapter 4: Further Topics on Random Variables: Transforms (Moment Generating Functions) 　
12/21 　 Chapter 4: Further Topics on Random Variables: Transforms (Moment Generating Functions) HW-4 (Due 12/28)
Variants of the Problems in pp. 14, 15, 16 of Lecture 10
12/24 　 Chapter 4: Further Topics on Random Variables: Convolutions, Conditional Expectation and Variance 　
12/28 　 Quiz 4 (1:10~3:10 p.m.) Scope: Sections 3.6 to 4.1
1/1 　 Holiday 　
1/4 　 Discussion of Quizzes 3 & 4, HW 3 & 4 　
1/8 　 Chapter 4: Further Topics on Random Variables: Convolutions, Conditional Expectation and Variance 　
1/11 　 Chapter 4: Further Topics on Random Variables: Sum of a Random Number of Random Variables, etc.
Quiz 5 (Take-Home Exercise) 		　
1/15 　 Final ( Good Luck ! ) Scope: Sections 3.1 to 4.4

Textbook:
     1.   D. P. Bertsekas, J. N. Tsitsiklis, “Introduction to Probability,” Athena Scientific, 2002.

References:
    1.   William C. Navidi, “Statistics for Engineers and Scientists,” McGraw-Hill, 2007.
     2.   Prem S. Mann, “Introductory Statistics,” Wiley, 2006.