2016 Probability Theory and Statistics

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Academic unit or major
Undergraduate major in Mechanical Engineering
Sakaguchi Motoki  Shimura Masayasu 
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Course description and aims

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.

Student learning outcomes

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.


Mean, standard deviation, sample, parameter, binominal distribution, Poisson distribution, normal distribution, probability density, maximum likelihood estimation, interval estimation

Competencies that will be developed

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/Required learning

  Course schedule Required learning
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 Understand statistical test and typical statistics used in procedure of the test
Class 8 Final exam and explanation Deepen understanding probability and statistics


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)

Assessment criteria and methods

Students' knowledge of probability and statistics will be assessed.
Final exams 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 (i.e., required knowledge, skills, courses, etc.)

Students are expected to have successfully completed both Calculus I (LAS.M101) and Calculus II (LAS.M105) or have equivalent knowledge.

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