## Course Title : Probabilistic and Statistical Analysis and Exercises

Code 35050 2nd year Tuesday・3-4 Kyotsu2 2 English Kim, Sunmin (Assoc. Prof., Graduate School of Eng.),

### 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 concepts and basic theorems of probability, probability distributions and their uses, statistical estimation and testing, and multivariate analysis.

Evaluation is based on written tests (midterm exam: 40%, final exam: 40%), assignment (10%), and attendance (10%).

### Course Goals

The goal is to understand fundamental theory of probability and to be capable of using well-known distributions in analysis and design. It is also required that students acquire knowledge of fundamentals of statistical 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 approaches in global engineering and in other engineering fields.
Basic theory of probabilistic analysis 4 The concepts and basic theories of probability: Conditional probability, Bayes’ theorem and total probability. Random variables: probability mass function (PMF), probability density function (PDF), cumulative distribution function (CDF), moment generating function, characteristic function, multidimensional probability 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, geometric distribution (return period), etc.
Statistical estimation and testing 3 Basic theory on sampling. Chi-square distribution, t- distribution, and F-distribution. Methods for statistical estimation and testing.
Multivariate analysis 2 Basic methods in multivariate analysis: regression analysis and principal component analysis.
Computer-based simulation methods in probability 1 Introduction to the computer-based simulation methods such as Monte-Carlo simulation, will be given.

### Textbook

Not specified. Some handout materials will be provided during the class.

### Textbook(supplemental)

A.H.S. Ang and W.H. Tang: Probability Concepts in Engineering: Emphasis on Applications in Civil and Environmental Engineering.

### Prerequisite(s)

Prerequisite courses are calculus and linear algebra.

Self-review is strongly recommended after each lecture.