HB230000 Exercises in Probability and Mathematical Statistics A

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HB230000 Subject Classification Specialized Education

Subject Name 確率・統計Ａ演習

Subject Name
（Katakana）カクリツ・トウケイAエンシュウ

Subject Name in
English Exercises in Probability and Mathematical Statistics A

Instructor ODA RYOYA

Instructor
(Katakana) オダ　リョウヤ

Campus Higashi-Hiroshima Semester/Term 3rd-Year, First Semester, 2Term

Days, Periods, and Classrooms (2T) Tues1-2,Fri3-4：SCI E209

Lesson Style Seminar Lesson Style
(More Details) 　

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

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Probability space, conditional probability, random variable, distribution, expectation, conditional expectation, characteristic function

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
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
・To acquire skills to formulate and solve mathematical questions.

Class Objectives
/Class Outline To understand concepts and properties of probability space, random variable and distribution

Class Schedule lesson1 Review of set theory
lesson2 Definition of probability space 1 (sample space and event, limit set)
lesson3 Definition of probability space 2 (probability measure, basic properties of probability measure)
lesson4 Construction of probability space
lesson5 Distribution of random variable (definition, distribution function)
lesson6 Independence of multivariate random variables
lesson7 Mid-term examination
lesson8 Distribution of discrete random variable
lesson9 Distribution of continuous random variable
lesson10 Distributions of discrete and continuous multivariate random variables
lesson11 Expectation of random variable and tis basic properties
lesson12 Feature values of distribution
lesson13 Conditional distribution
lesson14 Conditional expectation
lesson15 Characteristic function

Mid-term and final examinations will be held jointly with Probability and Mathematical Statistics A (lecture).
Quizzes and reports will be assigned as necessary.

Text/Reference
Books,etc. Book of reference:
確率・統計の数学的基礎（藤越康祝，若木宏文，柳原宏和著，広大出版, 電子版）, 数理統計学（竹内啓著，東洋経済出版）

PC or AV used in
Class,etc. 　

(More Details)

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review You should solve many exercise problems in the handout as possible by yourself. You should not copy someone's solutions.

Requirements I recommend taking the lecture on Probability & Mathematical Statistics A at the same time.

Grading Method The results of the answered exercises, quizzes and reports, as well as the results of the examinations of the lectures if they are taken at the same time as the lectures, are also taken into account in the decision.

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 Science
Lecture Code	HB230000	Subject Classification	Specialized Education
Subject Name	確率・統計Ａ演習
Subject Name （Katakana）	カクリツ・トウケイAエンシュウ
Subject Name in English	Exercises in Probability and Mathematical Statistics A
Instructor	ODA RYOYA
Instructor (Katakana)	オダ　リョウヤ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Tues1-2,Fri3-4：SCI E209
Lesson Style	Seminar	Lesson Style (More Details)

Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Probability space, conditional probability, random variable, distribution, expectation, conditional expectation, characteristic function
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 （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). ・To acquire skills to formulate and solve mathematical questions.
Class Objectives /Class Outline	To understand concepts and properties of probability space, random variable and distribution
Class Schedule	lesson1 Review of set theory lesson2 Definition of probability space 1 (sample space and event, limit set) lesson3 Definition of probability space 2 (probability measure, basic properties of probability measure) lesson4 Construction of probability space lesson5 Distribution of random variable (definition, distribution function) lesson6 Independence of multivariate random variables lesson7 Mid-term examination lesson8 Distribution of discrete random variable lesson9 Distribution of continuous random variable lesson10 Distributions of discrete and continuous multivariate random variables lesson11 Expectation of random variable and tis basic properties lesson12 Feature values of distribution lesson13 Conditional distribution lesson14 Conditional expectation lesson15 Characteristic function Mid-term and final examinations will be held jointly with Probability and Mathematical Statistics A (lecture). Quizzes and reports will be assigned as necessary.
Text/Reference Books,etc.	Book of reference: 確率・統計の数学的基礎（藤越康祝，若木宏文，柳原宏和著，広大出版, 電子版）, 数理統計学（竹内啓著，東洋経済出版）
PC or AV used in Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	You should solve many exercise problems in the handout as possible by yourself. You should not copy someone's solutions.
Requirements	I recommend taking the lecture on Probability & Mathematical Statistics A at the same time.
Grading Method	The results of the answered exercises, quizzes and reports, as well as the results of the examinations of the lectures if they are taken at the same time as the lectures, are also taken into account in the decision.
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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