### 2022　Probability theory (TSE)

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Undergraduate major in Transdisciplinary Science and Engineering
Instructor(s)
Chiba Satoshi
Class Format
Lecture    (Livestream)
Media-enhanced courses
Day/Period(Room No.)
Mon1-2(S223)  Thr1-2(S223)
Group
-
Course number
TSE.M301
Credits
2
2022
Offered quarter
2Q
Syllabus updated
2022/4/4
Lecture notes updated
-
Language used
English
Access Index

### Course description and aims

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.

### Student learning outcomes

to understand why various quantities are observed involving probability distributions, and to understand their stochastic nature to data analysis

### Course taught by instructors with work experience

How instructors' work experience benefits the course ✔ Applicable Stochastic process in quantum mechanics and experimental nuclear physics

### Keywords

Probability, probability distributions, stochastic variables, Bayes' theorem, moment-generating functions, normal distributions, covariance, least-squares method, stochastic process

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

Lecture based on power point, small examinations

### Course schedule/Required learning

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

### Out-of-Class Study Time (Preparation and Review)

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.

None

### Reference books, course materials, etc.

A.H-S. Ang and W.H. Tang, Probability Concepts in Engineering, Emphasis on Applications in Civil & Environmental Engineering, Maruzen & Wiley

### Assessment criteria and methods

Based on small test shown at the end of each lecture and submitted as a report, and a final report.

### Related courses

• ICT.M202 ： Probability and Statistics (ICT)

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