This lecture aims at making students to understand what is probability, why it is important, some important theorems on probability distributions and stochastic processes including Brownian motion and financial market.
to understand why various quantities are observed involving probability distributions, and to understand their stochastic nature to data analysis
|✔ Applicable||How instructors' work experience benefits the course|
|Stochastic process in quantum mechanics and experimental nuclear physics|
Probability, probability distributions, stochastic variables, Bayes' theorem, moment-generating functions, normal distributions, covariance, least-squares method, stochastic process
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
Lecture based on power point, small examinations
|Course schedule||Required learning|
|Class 1||Guidance and Introduction||Shown at the end of the lecture|
|Class 2||Intuitive introduction of sample space, events and probability||Shown at the end of the lecture|
|Class 3||σ-additive class, Probability distribution functions, expectation, variance, and higher moments||Shown at the end of the lecture|
|Class 4||Normal distribution, covariance matrix||Shown at the end of the lecture|
|Class 5||Conditional probability, Bayes theorem, independence of events and random variables, and conditional expectation value||Shown at the end of the lecture|
|Class 6||Moment generating function, characteristic function, cumulant generating function and equivalent probability measures||Shown at the end of the lecture|
|Class 7||A few probability distributions and their relations||Shown at the end of the lecture|
|Class 8||Central limit theorem and important inequalities||Shown at the end of the lecture|
|Class 9||Various convergences in probability theory and law of large numbers||Shown at the end of the lecture|
|Class 10||Stochastic process : random walk and concept of martingale||Shown at the end of the lecture|
|Class 11||Brownian motion||Shown at the end of the lecture|
|Class 12||Stieltjes integral and Ito ̂ integral||Shown at the end of the lecture|
|Class 13||Ito ̂ process||Shown at the end of the lecture|
|Class 14||Stochastic theory of financial market||Shown at the end of the lecture|
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
A.H-S. Ang and W.H. Tang, Probability Concepts in Engineering, Emphasis on Applications in Civil & Environmental Engineering, Maruzen & Wiley
Based on small test shown at the end of each lecture and submitted as a report, and a final report.