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School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Information and Communications Engineering
- Instructor(s)
- Uyematsu Tomohiko Kobayashi Takao
- Class Format
- Lecture / Exercise
- Media-enhanced courses
- Day/Period(Room No.)
- Mon1-4(S422) Thr1-2(S422)
- Group
- -
- Course number
- ICT.M202
- Credits
- 3
- Academic year
- 2017
- Offered quarter
- 1Q
- Syllabus updated
- 2017/3/17
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This course focuses on the fundamentals of probability and statistics which are used in various research areas such as model for digital communication, analysis of genome, and statistical analysis of big data. This course provides not only mathematical foundation of probability and statistics, but also practical methods to apply these mathematical knowledge.
Student learning outcomes
At the end of this course, students will be able to understand the following concepts:
1) The probability theory (probability axioms, expected value, variance, and moment generating function)
2) Multidimensional probability distribution, statistical independence, and correlation
3) Normal distribution and binomial distribution
4) Law of large numbers and central limit theorem
5) Hypothesis testing, point estimation, interval estimation
6) Bayesian statistics
Keywords
probability axioms, expected value, variance, moment generating function, multidimensional probability distribution, statistical independence, correlation, normal distribution, binomial distribution, law of large numbers, central limit theorem, hypothesis testing, point estimation, interval estimation, Bayesian statistics
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Towards the end of class, students are given exercise problems related to what is taught on that day to solve. In the exercise class, students are given advanced or practical problems related to the previous lecture classes.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Lecture 1: Basic mathematical knowledge | Peruse chapter 1 of the textbook. |
| Class 2 | Lecture 2: Probability | Peruse chapter 2 of the textbook. |
| Class 3 | Exercise 1 | Review Lectures 1 and 2. |
| Class 4 | Lecture 3: Random variables 1 | Peruse the first half of chapter 3 of the textbook. |
| Class 5 | Lecture 4: Random variables 2 | Peruse the last half of chapter 3 of the textbook. |
| Class 6 | Exercise 2 | Review Lectures 3 and 4 |
| Class 7 | Lecture 5: Joint probability distribution, covariance, and correlation coefficient | Peruse the last half of chapter 3 of the textbook. |
| Class 8 | Lecture 6: Binomial distribution and Poisson distribution | Peruse the first half of chapter 4 of the textbook. |
| Class 9 | Exercise 3 | Review Lectures 5 and 6 |
| Class 10 | Lecture 7: Central limit theorem and normal distribution | Peruse the last half of chapter 4 of the textbook. |
| Class 11 | Lecture 8: Distribution of samples and statistics | Peruse the first half of chapter 5 of the textbook. |
| Class 12 | Exercise 4 | Review Lectures 7 and 8 |
| Class 13 | Lecture 9: Normal population | Peruse the last half of chapter 5 of the textbook. |
| Class 14 | Lecture 10: Hypothesis testing | Peruse Section 6.3 of the textbook. |
| Class 15 | Exercise 5 | Review Lectures 9 and 10 |
| Class 16 | Lecture 10: Parameter estimation | Peruse Section 6.4 of the textbook. |
| Class 17 | Lecture 10: Point estimation and maximum likelihood estimation | Peruse Section 6.1 of the textbook. |
| Class 18 | Exercise 6 | Review Lectures 11 and 12 |
| Class 19 | Lecture 13: Interval estimation | Peruse Section 6.2 of the textbook. |
| Class 20 | Lecture 14: Least square method and estimation of correlation coefficient | Peruse Section 6.6 of the textbook. |
| Class 21 | Exercise 7 | Review Lectures 13 and 14 |
| Class 22 | Lecture 15: Bayesian statistics | None |
| Class 23 | Lecture 16: Review | Review all Lectures |
Textbook(s)
Junkichi Satsuma, Probability and Statistics, Iwanami, 1989. (Japanese)
Reference books, course materials, etc.
All materials used in class can be found on OCW-i.
Assessment criteria and methods
Student learning outcomes are evaluated by the results of exercises (20%), small examinations (40%), and the final examination (40%).
Related courses
- LAS.M101 ： Calculus I / Recitation
- LAS.M105 ： Calculus II
- LAS.M107 ： Calculus Recitation II
- LAS.M102 ： Linear Algebra I / Recitation
- LAS.M106 ： Linear Algebra II
- LAS.M108 ： Linear Algebra Recitation II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
No prerequisites.
