KA111001 Fundamentals of Probability Theory

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Informatics and Data Science

Lecture Code KA111001 Subject Classification Specialized Education

Subject Name 確率論基礎

Subject Name
（Katakana）カクリツロンキソ

Subject Name in
English Fundamentals of Probability Theory

Instructor DOHI TADASHI

Instructor
(Katakana) ドヒ　タダシ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  Second Semester,  4Term

Days, Periods, and Classrooms (4T) Weds1-4：IAS L102

Lesson Style Lecture Lesson Style
(More Details) 　

This lecture focuses on the fundamental theory of probability, and summarizes the definition of random variable, the representative probability distributions, their related probability measures such as mean and variance, and the fundamental extreme theory.

Credits 2.0 Class Hours/Week 　 Language of Instruction B : Japanese／English

Course Level 1 : Undergraduate Introductory

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students 1st degree undergraduate student

Keywords probability theory, random variable, probability distribution

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Program of Electrical,Systems and Information Engineering
（Abilities and Skills）
・Concepts, knowledge and methods which are the basis for studies related to electrical,  systems, and information engineering.
・Concepts, knowledge and methods which are the basis for studies related to electrical, systems, and information engineering.

Computer Science Program
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Data Science Program
（Knowledge and Understanding）
・D1. Knowledge and ability to understand the theoretical framework of statistics and data analysis and to analyze qualitative/quantitative information of big data accurately and efficiently.
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Intelligence Science Program
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Class Objectives
/Class Outline There are many uncertain events around us. The probability theory aims at dealing with such uncertain events quantitatively and is widely used in not only informatics and data science field but also natural science, engineering and social science. This lecture focuses on the fundamental theory of probability theory, and summarizes the representative probability distributions and their related probability measures such as mean, variance, moments and integral transforms.

The aim of this lecture is given in the following:

1. Review the classical probability theory with combinatorial probability and understand the basic concept of random variable and its related metrics. Here, students learn how to understand the intuitive but essential image on ``probability'' without introducing the probability measure theory.
2. Given an arbitrary probability distribution function, calculate the mean, variance, and the higher moments. Also, learn how to get the Stieltjes convolution of probability distribution functions and the integral transform such as characteristic function.
3. Learn some advanced topics such as stochastic ordering, aging properties and the extreme theory including the large number's law and the central limit theorem.

Class Schedule lesson1 Introduction
lesson2 Sample space and event
lesson3 Definitions of probability and random variable
lesson4 Classical probability theory based on combination
lesson5 Random variable and probability distribution
lesson6 Mean, variance, moments and integral transforms
lesson7 Multivariate random variable
lesson8 mid-term exam.
lesson9 Representative distributions (1): Discrete probability distribution
lesson10 Representative distributions (2): Continuous probability distribution
lesson11 Representative distributions (3): Normal probability distribution and its related topics
lesson12 Multivariate probability distribution
lesson13 Stieltjes convolution
lesson14 Stochastic order and aging properties
lesson15 Probability inequalities and extreme theory

Mid-term exam., final exam. and report

Text/Reference
Books,etc. Probability and Statistics in Engineering, Fumio Ohi, Suuri Kougakusha

PC or AV used in
Class,etc. 　

(More Details) Text book and power point slides

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Recommended to review the contents after joining the class because each class in this course is mutually related from each other.

Requirements

Grading Method The credit will be evaluated based on the final exam (possibly mid-term-exam). and the reports, where 60/100 point is the minimum requirement. The attainability will be evaluated from the view points of (i) fundamental knowledge of probability theory, (ii) applicability of probability theory to quantify uncertain events, (iii) computation skill of probability and its associated measures.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	School of Informatics and Data Science
Lecture Code	KA111001	Subject Classification	Specialized Education
Subject Name	確率論基礎
Subject Name （Katakana）	カクリツロンキソ
Subject Name in English	Fundamentals of Probability Theory
Instructor	DOHI TADASHI
Instructor (Katakana)	ドヒ　タダシ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Weds1-4：IAS L102
Lesson Style	Lecture	Lesson Style (More Details)
This lecture focuses on the fundamental theory of probability, and summarizes the definition of random variable, the representative probability distributions, their related probability measures such as mean and variance, and the fundamental extreme theory.
Credits	2.0	Class Hours/Week		Language of Instruction	B : Japanese／English
Course Level	1 : Undergraduate Introductory
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	1st degree undergraduate student
Keywords	probability theory, random variable, probability distribution
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Program of Electrical,Systems and Information Engineering （Abilities and Skills）・Concepts, knowledge and methods which are the basis for studies related to electrical, systems, and information engineering. ・Concepts, knowledge and methods which are the basis for studies related to electrical, systems, and information engineering. Computer Science Program （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. ・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis. Data Science Program （Knowledge and Understanding）・D1. Knowledge and ability to understand the theoretical framework of statistics and data analysis and to analyze qualitative/quantitative information of big data accurately and efficiently. （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. ・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis. Intelligence Science Program （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. ・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.
Class Objectives /Class Outline	There are many uncertain events around us. The probability theory aims at dealing with such uncertain events quantitatively and is widely used in not only informatics and data science field but also natural science, engineering and social science. This lecture focuses on the fundamental theory of probability theory, and summarizes the representative probability distributions and their related probability measures such as mean, variance, moments and integral transforms. The aim of this lecture is given in the following: 1. Review the classical probability theory with combinatorial probability and understand the basic concept of random variable and its related metrics. Here, students learn how to understand the intuitive but essential image on ``probability'' without introducing the probability measure theory. 2. Given an arbitrary probability distribution function, calculate the mean, variance, and the higher moments. Also, learn how to get the Stieltjes convolution of probability distribution functions and the integral transform such as characteristic function. 3. Learn some advanced topics such as stochastic ordering, aging properties and the extreme theory including the large number's law and the central limit theorem.
Class Schedule	lesson1 Introduction lesson2 Sample space and event lesson3 Definitions of probability and random variable lesson4 Classical probability theory based on combination lesson5 Random variable and probability distribution lesson6 Mean, variance, moments and integral transforms lesson7 Multivariate random variable lesson8 mid-term exam. lesson9 Representative distributions (1): Discrete probability distribution lesson10 Representative distributions (2): Continuous probability distribution lesson11 Representative distributions (3): Normal probability distribution and its related topics lesson12 Multivariate probability distribution lesson13 Stieltjes convolution lesson14 Stochastic order and aging properties lesson15 Probability inequalities and extreme theory Mid-term exam., final exam. and report
Text/Reference Books,etc.	Probability and Statistics in Engineering, Fumio Ohi, Suuri Kougakusha
PC or AV used in Class,etc.
(More Details)	Text book and power point slides
Learning techniques to be incorporated
Suggestions on Preparation and Review	Recommended to review the contents after joining the class because each class in this course is mutually related from each other.
Requirements
Grading Method	The credit will be evaluated based on the final exam (possibly mid-term-exam). and the reports, where 60/100 point is the minimum requirement. The attainability will be evaluated from the view points of (i) fundamental knowledge of probability theory, (ii) applicability of probability theory to quantify uncertain events, (iii) computation skill of probability and its associated measures.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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