Course title
330115002
Probability and Statistics

 NAKATSU Tomonori
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
Mathematical Sciences Course DP-4・1 研究者・技術者としての基礎的素養
代数、幾何、解析、応用数学、情報数学などの専門知識を修得し、課題を抽象化して数理的な問題設定をすると共に、適切な理論的考察・計算的手法を用いて問題解決策を構築できる。
Mathematical Sciences Course DP-4・2 キャリアを見据えた高度な専門知識
現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。
Purpose of class
Learn basics of Probability and Statistics
Course description
Lectures on basics of Probability and Statistics
Goals and objectives
  1. Lean basics of probability such as random variable, expectation, variance so on.
  2. Lean how to compute the expectation and variance.
  3. Lean basics of statistics.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term exam Final exam Total.
1. 20% 10% 30%
2. 30% 10% 40%
3. 30% 30%
Total. 50% 50% -
Evaluation method and criteria
Mid-term report and Final report
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Introduction Review of lectures 180minutes
2. Discrete probability space, Conditional probability Review of lectures 180minutes
3. Bayes’ theorem, Discrete random variable Review of lectures 180minutes
4. Probability law,
Important distributions: Binomial distribution, Geometric distribution, Poisson distribution 		Review of lectures 180minutes
5. Expectation and variance of discrete random variables, Properties of expectation and variance
Expectation and variance of important distributions 		Review of lectures 180minutes
6. Expectation and variance of important distributions
A model for stock price: binomial model 		Review of lectures 180minutes
7. General probability space, random variable, distribution and probability density function Review of lectures 180minutes
8. Important distributions: Normal distribution, Uniform distribution, Exponential distribution
Expectation and variance of important distributions
On Mid-term report 		Review of lectures 180minutes
9. Law of large numbers, Central limit theorem Review of lectures 180minutes
10. Basics of statistics Review of lectures 180minutes
11. Sampling distribution, Interval estimation Review of lectures 180minutes
12. t-distribution
Interval estimation 		Review of lectures 180minutes
13. Chi-square distribution
Convolution 		Review of lectures 180minutes
14. Chi-square distribution, F-distribution
On Final report 		Review of lectures 270minutes
Total. - - 2610minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
The Others 授業内あるいは授業外
Textbooks and reference materials
The following would be helpful:
「確率・統計入門」小針晛宏著、岩波書店
Prerequisites
Office hours and How to contact professors for questions
  • e-mail
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
Most classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
Applicable Nakatsu worked at a financial institute for 4 years.
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 8.DECENT WORK AND ECONOMIC GROWTH
  • 16.PEACE, JUSTICE AND STRONG INSTITUTIONS
Last modified : Mon Mar 23 04:07:08 JST 2026