2020 Faculty Courses School of Engineering Undergraduate major in Mechanical Engineering
Probability Theory and Statistics
- Academic unit or major
- Undergraduate major in Mechanical Engineering
- Instructor(s)
- Motoki Sakaguchi / Masayasu Shimura
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 1-2 Fri (I121,I123,124)
- Class
- -
- Course Code
- MEC.B231
- Number of credits
- 100
- Course offered
- 2020
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
Syllabus
Course overview and goals
In this course, firstly typical probability distributions and statistics are lectured after a short review of basic of probability. Secondly, estimation and verification of parameters are learned. Based on the knowledge of statistics, explanation of characteristics of population is studied.
A variety of knowledge on mathematics are required to resolve issues and make progresses in mechanical engineering. Probability and statistics is not only important for following a lot of courses in mechanical engineering, but also indispensable for data handling and evaluation in researches, developments and production after your graduation, especially in the era of big data. Students are expected to take this course.
Course description and aims
By the end of this course, students will be able to:
1) Explain typical sample statistics and probability distributions
2) Calculate parameters by means of estimation and verification
3) Explain characteristics of target population by means of statistics.
Keywords
Mean, standard deviation, sample, parameter, binominal distribution, Poisson distribution, normal distribution, probability density, maximum likelihood estimation, interval estimation
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The course is taught in lecture style. Exercise problems will be assigned after the fourth class. Required learning should be completed outside of the classroom for preparation and review purposes.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction, event and probability |
Understand relation between data and sample space，definition of event and probability, Bayes' theorem |
| Class 2 | Random variable and probability distribution |
Understand random variable, probability distribution, probability density function |
| Class 3 | Probability distribution, mean and standard deviation, central limit theorem |
Understand mean and standard deviation, moment-generating function, normal distribution, central limit theorem |
| Class 4 | Examples of probability distribution |
Understand probability distributions such as binominal, Poisson and normal distributions |
| Class 5 | Sample, statistic and sample distribution |
Understand relation between sample and population，relation between sample statistics and parameter, χ2 and t distributions |
| Class 6 | Estimation |
Understand maximum likelihood estimation and interval estimation |
| Class 7 | Statistical test |
statistical test and typical statistics used in procedure of the test |
Study advice (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.
Textbook(s)
Materials will be provided if they are required.
Reference books, course materials, etc.
Robert S. Witte, John S. Witte, "Statistics", Hoboken : John Wiley and Sons, Inc., (2015)
Evaluation methods and criteria
Students' knowledge of probability and statistics will be assessed.
Final report 70%, exercise problems 30%.
Related courses
- MEC.B211 ： Ordinary Differential Equations
- MEC.B213 ： Partial Differential Equations
- MEC.B212 ： Complex Function Theory
- MEC.B214 ： Vector Analysis
- MEC.B232 ： Fundamentals of Numerical Analysis
Prerequisites
Students are expected to have successfully completed both Calculus I (LAS.M101) and Calculus II (LAS.M105) or have equivalent knowledge.