授業の目的 【日本語】
Goals of the Course(JPN) | | | 本講義では，確率統計および演習で学んだ確率統計の理論を基礎におき，正規母集団に関する標本分布の性質を理解する．具体的には，カイ二乗分布・t分布・F分布といった標本分布を学び，点推定・区間推定および仮説検定の各種手法を修得する．さらに，適合度検定・独立性検定を理解するとともに，最小二乗法と相関係数の推定・検定についても学ぶ． |
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授業の目的 【英語】
Goals of the Course | | | Building on the theory of probability and statistics studied in previous courses, students will understand the properties of sampling distributions related to normal populations. Specifically, they will study sampling distributions such as the chi-squared distribution, t-distribution, and F-distribution, and acquire various methods of point estimation, interval estimation, and hypothesis testing. Furthermore, they will understand goodness-of-fit tests and independence tests, and study the method of least squares along with estimation and testing of correlation coefficients. |
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到達目標 【日本語】
Objectives of the Course(JPN) | | | 数理統計学では，正規母集団に関するカイ二乗分布・t分布・F分布などの代表的な標本分布を理解するとともに，実験結果や測定値などのデータから母集団の性質を合理的に推定・検定する方法を学ぶ．具体的には，点推定・区間推定，仮説検定，適合度検定・独立性検定，および最小二乗法と相関係数の推定・検定といった統計的手法の原理と利用法を修得する． |
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到達目標 【英語】
Objectives of the Course | | | In this course on mathematical statistics, students will understand representative sampling distributions related to normal populations, such as the chi-squared distribution, t-distribution, and F-distribution, and learn methods for rationally estimating and testing the properties of populations from experimental results and measurement data. Specifically, they will acquire the principles and practical applications of statistical methods including point estimation, interval estimation, hypothesis testing, goodness-of-fit tests, independence tests, and the method of least squares along with estimation and testing of correlation coefficients. |
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授業の内容や構成
Course Content / Plan | | 本講義では，数理統計学の基本的な概念を学ぶ．具体的には，カイ二乗分布・t分布・F分布などの代表的な標本分布，点推定・区間推定，仮説検定，適合度・独立性の検定，および最小二乗法と相関係数の推定・検定等を扱う．
1. 正規母集団
2. カイ二乗分布
3. t分布
4. F分布
5. 点推定＆区間推定
6. 仮説と検定＆母数の検定
7. 適合度と独立性の検定
8. 最小二乗法と相関係数の推定・検定 | This course covers the fundamental concepts of mathematical statistics. Specifically, topics include representative sampling distributions such as the chi-squared, t-, and F-distributions, point estimation and interval estimation, hypothesis testing, goodness-of-fit and independence tests, and the method of least squares and estimation/testing of correlation coefficients, among others.
1. Normal Population
2. Chi-squared Distribution
3. t-Distribution
4. F-Distribution
5. Point Estimation and Interval Estimation
6. Hypothesis Testing and Parameter Testing
7. Goodness-of-fit Test and Independence Test
8. Method of Least Squares and Estimation/Testing of Correlation Coefficients |
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履修条件・関連する科目
Course Prerequisites and Related Courses | | | SIS-01-2009-J（確率統計および演習）を習得していることを前提とする． | |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | | 講義の出席20％，講義で課す課題80％，合計100点満点で60点以上を合格とする． | |
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教科書・参考書
Textbook/Reference book | | | 理工系の数学入門コース7 確率・統計，薩摩順吉著，岩波書店，1988年． | |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | | 講義において説明した理論を理解するために必要に応じて課題を与える． | |
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授業開講形態等
Lecture format, etc. | | |
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遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class) | | |
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