HB330000 Probability and Mathematical Statistics C

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Science

Lecture Code HB330000 Subject Classification Specialized Education

Subject Name 確率・統計Ｃ

Subject Name
（Katakana）カクリツ・トウケイC

Subject Name in
English Probability and Mathematical Statistics C

Instructor OKAMOTO MAMORU

Instructor
(Katakana) オカモト　マモル

Campus Higashi-Hiroshima Semester/Term 4th-Year, Second Semester, 3Term

Days, Periods, and Classrooms (3T) Mon3-4,Weds7-8：AdSM 405N

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

To be announced by the teacher.

Credits 2.0 Class Hours/Week 4 Language of Instruction J : Japanese

Course Level 4 : Undergraduate Advanced

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords probability space, random variable, distribution, expectation, independence, convergence of random variables, limit theorems

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) Mathematics
（Knowledge and Understanding）
・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics.

Class Objectives
/Class Outline Measure-theoretic probability theory

Class Schedule 1. Probability space
2. Expectation
3. Lp spaces
4. Convergence of random variables
5. Independence
6. Kolmogorov extension theorem
7. Kolmogorov's zero–one law
8. Strong law of large numbers
9. Central limit theorem
10. Proof of Central limit theorem
11. Convergence in law
12. Tightness
13. Characteristic functions
14. Application of characteristic functions
15. Summary

Text/Reference
Books,etc. R. Durrett: Probability, Cambridge University Press, 5th ed

PC or AV used in
Class,etc. moodle

(More Details)

Learning techniques to be incorporated

Suggestions on
Preparation and
Review For each lesson, make sure you can state definitions, notation, and theorem statements accurately, and that you can explain the flow and main ideas of theorem proofs.

Requirements

Grading Method Report

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	2026Year	School/Graduate School	School of Science
Lecture Code	HB330000	Subject Classification	Specialized Education
Subject Name	確率・統計Ｃ
Subject Name （Katakana）	カクリツ・トウケイC
Subject Name in English	Probability and Mathematical Statistics C
Instructor	OKAMOTO MAMORU
Instructor (Katakana)	オカモト　マモル
Campus	Higashi-Hiroshima	Semester/Term	4th-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Mon3-4,Weds7-8：AdSM 405N
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
To be announced by the teacher.
Credits	2.0	Class Hours/Week	4	Language of Instruction	J : Japanese
Course Level	4 : Undergraduate Advanced
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	probability space, random variable, distribution, expectation, independence, convergence of random variables, limit theorems
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)	Mathematics （Knowledge and Understanding）・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics.
Class Objectives /Class Outline	Measure-theoretic probability theory
Class Schedule	1. Probability space 2. Expectation 3. Lp spaces 4. Convergence of random variables 5. Independence 6. Kolmogorov extension theorem 7. Kolmogorov's zero–one law 8. Strong law of large numbers 9. Central limit theorem 10. Proof of Central limit theorem 11. Convergence in law 12. Tightness 13. Characteristic functions 14. Application of characteristic functions 15. Summary
Text/Reference Books,etc.	R. Durrett: Probability, Cambridge University Press, 5th ed
PC or AV used in Class,etc.	moodle
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	For each lesson, make sure you can state definitions, notation, and theorem statements accurately, and that you can explain the flow and main ideas of theorem proofs.
Requirements
Grading Method	Report
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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