Course Objectives

The aim of this course is to let students learn fundamentals of probability and statistics. And then the students can easily utilize probability and statistics method to analyze problems and carry on researches. Its contents include the Experiments, Models, and Probabilities, Sequential Experiments, Discrete Random Variables, Continuous Random Variables, Multiple Random Variables, Probability Models of Derived Random Variables, Conditional Probability Models, Random Vectors, Sums of Random Variables, The Sample Mean, Hypothesis Testing, Estimation of a Random Variable, and Stochastic Processes.

Textbooks

Required:

Roy D. Yates and David J. Goodman, “Probability & Stochastic Process”, 3rd edition, John Wiley & Sons, Inc., 2015.

Grading

• Attendance: 10%

• Homework: 20%

• Midterm: 35%

• Final Examination: 35%

Homework assignments must all be turned in at the beginning of class on the day they are due. For every day (or portion of a day) an assignment is late, 25% will be subtracted from its maximum point total. You may discuss strategies for solving the homework with your classmates. But please do your own homework.

All exams are closed book. (with open book option)

Course Outline

Week Content

1 Introduction

2 Experiments, Models, and Probabilities (Chapter 1)

3 Experiments, Models, and Probabilities (Chapter 1)

4 Sequential Experiments (Chapter 2)

5 Sequential Experiments (Chapter 2)

6 Discrete Random Variables (Chapter 3)

7 Discrete Random Variables (Chapter 3)

8 Continuous Random Variables (Chapter 4)

9 Continuous Random Variables (Chapter 4)

10 Midterm (Midterm on the above material)

11 Multiple Random Variables (Chapter 5)

12 Multiple Random Variables (Chapter 5)

13 Probability Models of Derived Random Variables (Chapter 6)

14 Conditional Probability Models (Chapter 7)

15 Conditional Probability Models (Chapter 7)

16 Sums of Random Variables (Chapter 9)

17 Sums of Random Variables (Chapter 9)

18 Final Exam (Final covers the whole course, but with an emphasis on Ch.5, Ch.6, Ch.7 & Ch.9)

Course Material

• Lecture notes

1. Ch1
2. Ch2
3. Ch3
4. Ch4
5. Ch5

• Homework Assignments

1. HW1
2. HW2
3. HW3
4. HW4
5. HW5