## Course Title : Probabilistic and Statistical Analysis and Exercises

Code 30030 2nd year 2 Japanese S.Tohno,E.Nakakita,T.Hori,M.Onishi,

### Course Description

Theory and methodology of probabilistic and statistical analysis is introduced as a basic tool to cope with uncertainty in natural and social systems dealt with in global engineering. The main topics are concept and basic theorems of probability, probability distributions and its use, statistical estimation and testing, and multivariate analysis.

### Grading

Grading is done based on the mark on regular examination. Performance in classes and exercises, marks in quiz and mid-term exams are also taken into account. Minimum passing grade is sixty percent.

### Course Goals

The goal is to understand fundamental theory of probability and to be capable of using well-known distributions to analysis and design. It is also required that students understand the fundamentals on population and samples, and principle of statistical estimation and testing.

### Course Topics

Theme Class number of times Description
Introduction 1 Role of probabilistic and statistical approach in global engineering and in other engineering fields.
Basic theory for probabilistic analysis 4 The concept and basic theory on probability: random variables, probability mass function, probability density function, distribution function, Bayes’ theorem, moment generating function, characteristic function, multi-dimensional distribution, transform of random variables.
Probability distribution models 4 Probability distributions often used in global engineering are introduced: Bernoulli series and binomial distribution, Poisson series and distribution, normal distribution, return period.
Statistical estimation and testing 3 Basic theory on sampling. Chi-square, t-, and F-distributions. Methods for statistical estimation and testing.
Multivariate analysis 2 Basic methods in multivariate analysis: regression analysis and principal component analysis.
Attainment check 1 Evaluation of the attaiment level.

### Textbook

Kitamura,S and Hori,T(eds.): An Introduction to Probability and Statistics for Engineering, Asakura Publishing Co., Ltd., 3,600 ### Textbook(supplemental)

Supplemental materials will be introduced in the class.

### Prerequisite(s)

Prerequisite courses are infinitesimal calculus and linear algebra.