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STAT201 Probability Theory and Applications

Instructor Name : Education Professor Kwong Koon Shing Email : kskwong@smu.edu.sg Tel : 6828-0834 Office : SOE/SOSS 05-059 COURSE DESCRIPTION The purpose of this course is to develop knowledge of the fundamental probability theory for quantitatively assessing the uncertain events. The focus in each teaching topic is on the applications of the probability concepts in everyday life. But practical problems encountered in actuarial science and finance are particularly emphasized. Topics include overview of probability, probability distributions, mathematical expectation, some special discrete distributions, some continuous distributions, functions of random variables, sampling distributions, jointly distributed random variables, Limit theorems and stochastic process. LEARNING OBJECTIVES The main objective of this course is to teach students probability which can be applied in everyday life or in other disciplines. The features of pedagogical approach used in this course are the followings:

Emphasize verbal interpretations of concepts and methodologies;

Explain theoretical results in laymans terms with minimum amount of mathematical proofs; Illustrate new concepts with real-life issues in other disciplines, such as economics, business,

finance, insurance and actuarial science etc. Specific real-life applications include: o Portfolio theory o Generating random variables and simulation o Utility function and insurance o Risk and insurance o Poisson/exponential modeling applied to real-world phenomena o Log-normal model applied to long-term stock returns o The Black-Scholes option pricing

PREREQUISITE STAT101 or STAT151 ASSESSMENT METHODS Class Participation : 10% Assignments : 20% Mid-term Test : 30% Final Examination : 40% Total : 100% ACADEMIC INTEGRITY All acts of academic dishonesty (including, but not limited to, plagiarism, cheating, fabrication, facilitation of acts of academic dishonesty by others, unauthorized possession of exam questions, or tampering with the academic work of other students) are serious offences.

School of Economics

Academic Year 2014-15 Term 1

2

All work (whether oral or written) submitted for purposes of assessment must be the students own work. Penalties for violation of the policy range from zero marks for the component assessment to expulsion, depending on the nature of the offense. When in doubt, students should consult the instructors of the course. Details on the SMU Code of Academic Integrity may be accessed at http://www.smuscd.org/resources.html. CLASS TIMINGS Class sessions are of 3-hour duration per week. Each session will involve a lecture and a discussion of assignments and class works.

RECOMMENDED TEXT AND READINGS

Ross, Sheldon, (2014), A First Course in Probability, 9

th edition, Prentice Hall. (If you have 7

th or 8

th

edition textbook, you may use it.)

SUPPLEMENTARY TEXT

Hull, John C, (2012), Options, Futures, and Other Derivatives, 8th edition, Prentice Hall.

WEEKLY LESSON PLAN This table provides a tentative course schedule which is subject to change.

Week Topics Chapter

1 Combinatorial Analysis, Overview of Probability, Conditional Probability and Independence

Ch 1 -- Ch 3

2 Practical Applications I Ch 1 Ch 3

3 Discrete Random Variables Ch 4

4 Continuous Random Variables Ch 5

5 Jointly Distributed Random Variables Ch 6

6 Practical Applications II Ch 4 Ch 6

7 Practical Applications III Ch 4 Ch 6

8 RECESS

9 Mid-term test

10 Properties of Expectation

Ch 7

11 Limit Theorems Ch 8

12 Practical Applications IV

13 Practical Applications V

14 Revision Week

15 Examination

Updated on 2 June, 2014