### 2017　Probability and Statistics (ICT)

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Undergraduate major in Information and Communications Engineering
Instructor(s)
Uyematsu Tomohiko  Kobayashi Takao
Course component(s)
Lecture / Exercise
Day/Period(Room No.)
Mon1-4(S422)  Thr1-2(S422)
Group
-
Course number
ICT.M202
Credits
3
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. 