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, measure theory, probability space Review of lectures 180minutes
2. Example 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. Conditional expectation, independence Review of lectures 180minutes
7. Mid-term exam and its review Review of lectures 270minutes
8. Weak law of large numbers Review of lectures 180minutes
9. Strong law of large numbers Review of lectures 180minutes
10. Central limit theorem 1 Review of lectures 180minutes
11. Central limit theorem 2 Review of lectures 180minutes
12. Discrete time martingales Review of lectures 180minutes
13. Summary and further topics: Brownian motion, Stochastic integral, Ito's formula, Stochastic differential equation, Mathematical finance 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
Relation to the environment
Non-environment-related course
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.
Last modified : Thu Mar 21 15:21:13 JST 2019