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 and how to compute the expectation using probability distributions
  2. Lear the proof of the law of large numbers
  3. Lear the proof of the central limit theorem
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Guidance, measurable space, probability space Review of lectures 180minutes
2. Examples and properties of probability space Review of lectures 180minutes
3. Random variable, distribution, expectation, variance, moment Review of lectures 180minutes
4. Useful inequalities and dominated convergence theorem Review of lectures 180minutes
5. Convergences of random variables Review of lectures 180minutes
6. Independence of events, σ-algebras, random variables Review of lectures 180minutes
7. Mid-term exam and its review Review of lectures 270minutes
8. Weak and strong law 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. Central limit theorem Review of lectures 180minutes
13. Proof of Central limit theorem Review of lectures 180minutes
14. Final exam and its review Review of lectures 270minutes
Total. - - 2700minutes
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% -
Evaluation method and criteria
Mid-term exam and Final exam (Depending on the situation, reports will be added to the evaluation)
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
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicatable
Applicatable 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
  • 12.RESPONSIBLE CONSUMPTION & PRODUCTION
Last modified : Sat Jun 20 04:13:20 JST 2020