Hiroshima University Syllabus |

Japanese

Academic Year 2022Year 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

EnglishFundamentals 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

ProgramCriterion referenced

EvaluationProgram 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 OutlineThere 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 reportText/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

ReviewRecommended 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.