## Course Title : Probabilistic and Statistical Analysis and Exercises

Code 35050 2nd year 1st term Tuesday・3-4 Kyoutsuu2 2 English Qureshi

### 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.

Grading is done based on the marks in 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 (60%).

### 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(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.