Course title
V06106003
Advanced Probability and Statistics

 NAKATSU Tomonori Click to show questionnaire result at 2018
Course description
Lectures on advanced Probability and Statistics
Purpose of class
Learn advanced Probability and Statistics, especially Law of large numbers and Central limit theorem
Goals and objectives
  1. Lean basics of probability
  2. Lear the proof of the law of large numbers
  3. Lear the proof of the central limit theorem
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term exam Final exam Total.
1. 45% 0% 45%
2. 5% 30% 35%
3. 0% 20% 20%
Total. 50% 50% -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Guidance, measurable space Review of lectures 180minutes
2. Probability space, examples and properties of probability Review of lectures 180minutes
3. Random variable and its properties Review of lectures 180minutes
4. Properties, limit and distribution of random variables Review of lectures 180minutes
5. Expectation of random variable, useful inequalities Review of lectures 180minutes
6. Convergence theorems, variance, moment
Convergences of random variables 		Review of lectures 180minutes
7. Convergence of random variables
Independence of events, σ-algebras 		Review of lectures 180minutes
8. Independence of random variables
Weak and strong laws of large numbers 		Review of lectures 180minutes
9. Proof of weak law of large numbers Review of lectures 180minutes
10. Borel-Cantelli lemma Review of lectures 180minutes
11. Proof of strong law of large numbers Review of lectures 180minutes
12. Characteristic function and its applications Review of lectures 180minutes
13. Proof of Central limit theorem Review of lectures 180minutes
14. Proof of Central limit theorem Review of lectures 180minutes
Total. - - 2520minutes
Evaluation method and criteria
Mid-term exam and Final exam (Depending on the situation, reports will be added to the evaluation)
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:
・「確率論」舟木直久著、朝倉書店
・「確率論」西尾真喜子、実教出版
Prerequisites
Nothing special
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
  • 1.NO POVERTY
  • 4.QUALITY EDUCATION
  • 8.DECENT WORK AND ECONOMIC GROWTH
Last modified : Thu Feb 27 10:50:40 JST 2025