| Academic Year |
2026Year |
School/Graduate School |
School of Informatics and Data Science |
| Lecture Code |
KA241301 |
Subject Classification |
Specialized Education |
| Subject Name |
数理統計学 |
Subject Name
（Katakana） |
スウリトウケイガク |
Subject Name in
English |
Mathematical Statistics |
| Instructor |
IMORI SHINPEI |
Instructor
(Katakana) |
イモリ シンペイ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
3rd-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Tues9-10,Thur9-10：SCI E210 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| Lecture |
| Credits |
2.0 |
Class Hours/Week |
4 |
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 |
B3 |
| Keywords |
low of large numbers, central limit theorem, population and sample, estimation |
| 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) | Computer Science Program
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
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 |
Study theorems on convergence of ramdom variable, derivation of the distribution of statistics, and estimations |
| Class Schedule |
Lesson 1: Review of foundations of probability and mathematical statistics
Probability space, distribution of random variables, expectation, and characteristic function.
Lesson 2: Convergence of random variables (1)
Convergence in probability and low of large numbers
Lesson 3: Convergence of random variables (2)
Convergence in distribution and central limit theorem
Lesson 4: Convergence of random variables (3)
Almost sure convergence and asymptotic theories
Lesson 5: Population distribution and statistical models
Population, population distribution, and statistical models
Lesson 6: Sample mean and sample variance (1)
Lesson 7: Sample mean and sample variance (2)
Lesson 8: Order statistics
Lesson 9: Estimation (1)
Point estimation, least square method, and univariate linear regression models
Lesson 10: Estimation (2)
Unbiased estimator and likelihood method
Lesson 11: Estimation (3)
Interval estimation 1
Lesson 12: Estimation (4)
Interval estimation 2
Lesson 13: Testing hypothesis (1)
Erros in testing hypothesis
Lesson 14: Testing hypothesis (2)
Testing hypothesis
Lesson 15: Summary
Examination
The class schedule may be changed due to the progress. |
Text/Reference
Books,etc. |
「確率・統計の数学的基礎」（藤越、若木、栁原著） |
PC or AV used in
Class,etc. |
Text, Microsoft Teams |
| (More Details) |
|
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Read the text book before each lecture and solve the problems in it. |
| Requirements |
Students who take this class should understand class contents of "Probability and Mathematical Statistics A" held in School of Science. |
| Grading Method |
Quiz and examination (and report if necessary) |
| 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. |