2022 Applied Probability and Statistical Theory

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Academic unit or major
Undergraduate major in Electrical and Electronic Engineering
Kajikawa Kotaro  Sakaguchi Kei 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue1-2(S221)  Fri1-2(S221)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

It is vital to acquire knowledge and skills in statistics and probability in various fields related to electrical engineering and information communication engineering. By combining lectures and exercises, the course enables students to understand and learn the fundamentals of mean, variance, characteristic function, etc. in the first part (probability) and those of unbiased estimation, maximum likelihood estimation, Bayesian inference, hypothesis testing, machine learning, etc. in the second part (statistics).
 The ability to derive statistically significant information will be very useful in the real world.

Student learning outcomes

Students will be able to learn how to analyze data in various fields related to electrical engineering and information communication engineering by using probablistic methods and statistical techniques. The course provides specific examples in engineering, which will give a deeper understanding. Many practical exercises and exams will enable students to acquire knowledge effectively.

Corresponding educational goals are:
(1) Specialist skills Fundamental specialist skills
(6) Firm fundamental specialist skills on electrical and electronic engineering, including areas such as electromagnetism, circuits, linear systems, and applied mathematics


Probability, Mean, Variance, Maximum likelihood estimation, Bayesian inference, Hypothesis testing, Machine learning

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills
・Fundamental specialist skills on EEE

Class flow

To cultivate practical ability, students are given many exercise problems, which are related to a previous class and a class on the day.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Permutations Understand the Permutations
Class 2 Conditional probability Calculate conditional probability.
Class 3 Mean and variance Calculate mean and variance
Class 4 Characteristic function Understand characteristic function
Class 5 Random variable and distribution I Understand random variable and distribution
Class 6 Random variable and distribution II Understand random variable and distribution
Class 7 Test level of understanding with exercise problems Test level of understanding for classes 1–6
Class 8 Statistical inference Understand data analysis by statistical inference
Class 9 Unbiased estimation Understand unbiased estimation
Class 10 Maximum likelihood estimation and Bayesian inference Learn how to perform maximum likelihood estimation and Bayesian inference
Class 11 Hypothesis testing, Classification, Machine learning Learn how to perform hypothesis test and classification
Class 12 Regression, Prediction, Machine learning Learn how to perform regression and prediction
Class 13 Stochastic process Understand stochastic process and method of data analysis
Class 14 Test level of understanding with exercise problems Test level of understanding for classes 8–13

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.



Reference books, course materials, etc.

Watanabe, Sumio, Noboru, Murata, Probability and statistics: a bridge to information science, Corona-sha; ISBN: 9784339060775 (in Japanese)
Ogura, Hisanao, stochastic process for physics and engineering, Corona-sha; ISBN: 9784339004229, 9784339004236 (in Japanese)
Shibata, Fumiaki, Probability and statistics, Iwanami-shoten; ISBN: 9784000079778 (in Japanese)
Baba, Noriyuki, Kuchii, Shigeru, Campus seminar: statistics, mathema-shuppan, ISBN: 9784907165314 (in Japanese)
Suyama, Atsushi, Machine learning based on Bayesian inference, Kodansha; ISBN: 9784061538320 (in Japanese)

Assessment criteria and methods

Students' knowledge of probability and statistical, and their ability to apply them to problems will be assessed.
Exam 50%, exercise problems 50%.

Related courses

  • LAS.M101 : Calculus I / Recitation
  • LAS.M105 : Calculus II
  • EEE.M211 : Fourier Transform and Laplace Transform
  • EEE.S341 : Communication Theory (Electrical and Electronic Engineering)

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed both Calculus I and Calculus II.


Contact by e-mail in advance.

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