Course Introduction

• Prerequisite：calculus
• Recommended for： sophomore
• Introduction：

This course is intedned as an elementary introduction to the theory of probability for students in mathematics. It attempts to present not only the mathematics of probability theory but also, through numerous examples, the many diverse possible applications of this subject. The prerequisite for this course is very fundamental, including the basic counting in high school and a one-year course in calculus.

• Syllabus：

1. Classical probability: Counting, axiom of probability, conditional probability, Bayes's formula and independent events 　 　
2. Random variables: Discrete and continuous random variables 　 　
3. Joint distributed random variables: Joint distributions, conditional distributions and independent random variables 　 　
4. Properties of expectation: Expectation, variance, moment, covariance, correlation and conditional expectation and variance　 　 　
5. Limiting theorems: Markov and Chebyshev's inequalities, the law of large numbers and the central limit theorem

• Reference：

1. Sheldon Ross, A first course in probability 8th Edition, 2009, Prentice Hall