### 2018　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.)
Mon3-6(S422)  Thr5-6(S422)
Group
-
Course number
ICT.M202
Credits
3
2018
Offered quarter
1Q
Syllabus updated
2018/3/20
Lecture notes updated
2018/6/13
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: Definition of probability Peruse chapter 2 of the textbook.
Class 3 Exercise 1 Review Lectures 1 and 2.
Class 4 Lecture 3: Bayes' theorem and random variables 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: Multi-dimensional random variable 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: Normal distribution and central limit theorem 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 1 through 7.
Class 13 Lecture 9: Normal population Peruse the last half of chapter 5 of the textbook.
Class 14 Exercise 5 Review Lectures 8 and 9
Class 15 Lecture 10: Statistical estimation Peruse Section 6.1 of the textbook.
Class 16 Lecture 11: Interval estimation and confidence level Peruse Section 6.2 of the textbook.
Class 17 Exercise 6 Review Lectures 10 and 11
Class 18 Lecture 12: Interval estimation 2 Peruse Section 6.2 of the textbook.
Class 19 Lecture 13: Hypothesis testing Peruse Section 6.3 of the textbook.
Class 20 Exercise 7 Review Lectures 12 and 13
Class 21 Lecture 14: Hypothesis testing2 Peruse Sections 6.4 and 6.5 of the textbook.
Class 22 Lecture 15: Review Review all Lectures
Class 23 Exercise 8 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. 