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Probability Methods in Civil Engineering

Overview

Instructor: Prof. Rajib Maity, Department of Civil Engineering, IIT Kharagpur.

The concept of probability and statistics is very important to solve various civil engineering problems. In this course, basic probability concepts and different probabilistic models will be discussed. The concept and definition of random variables and different functions of random variables will be covered in the initial part of the course. Afterward, the focus is given to commonly used probability distribution functions in civil engineering. Discussions on statistics and sampling are presented towards the last part of the course. In this part, goodness of fit tests, regression and correlation analyses, estimation of distribution parameters from statistics, hypothesis testing and their significance will be discussed. A brief introduction to copulas is also included in this course. Each topic is discussed with reference to different application problems and their solutions in different fields of civil engineering, such as Structural Engineering, Transportation Engineering, Water Resources and Environmental Engineering, Geotechnical Engineering etc.

Syllabus

Mod-01 Lec-01 Introduction - Role of Probability in Civil Engineering.
Mod-01 Lec-02 Random Events and Probability Concept.
Mod-01 Lec-03 Set Theory and Set Operations.
Mod-01 Lec-04 Axioms of Probability.
Mod-01 Lec-05 Probability of Events.
Mod-01 Lec-06 Concept and Defination of Random Variables.
Mod-01 Lec-07 Probability Distribution of Random Variables.
Mod-01 Lec-08 CDF and Descriptors of Random Variables.
Mod-01 Lec-09 Further Descriptors of Random Variables.
Mod-01 Lec-10 Discrete Probability Distribution.
Mod-01 Lec-11 Probability Distribution of Continuous RVs.
Mod-01 Lec-12 Probability Distribution of Continuous RVs (Contd...1).
Mod-01 Lec-13 Probability Distribution of Continuous RVs (Contd...2).
Mod-01 Lec-14 Functions of Single Random Variables.
Mod-01 Lec-15 Functions of Random Variables - Different Methods.
Mod-01 Lec-16 Functions of Random Variables - Different Methods (Contd.).
Mod-01 Lec-17 Expectation and Moments of Functions of RV.
Mod-01 Lec-18 Expectation and Moments of Functions of RV (Contd.).
Mod-01 Lec-19 Joint Probability Distribution.
Mod-01 Lec-20 Marginal Probability Distribution.
Mod-01 Lec-21 Conditional Probability Distribution.
Mod-01 Lec-22 Conditional Probability Distribution (Contd.).
Mod-01 Lec-23 Properties of Multiple Random Variables.
Mod-01 Lec-24 Properties of Multiple Random Variables (Contd.).
Mod-01 Lec-25 MGF of Multivariate RVs and Multivariate Probability Distributions.
Mod-01 Lec-26 Multivariate Distribution and Functions of Multiple Random Variables.
Mod-01 Lec-27 Functions of Multiple Random Variables (Contd...1).
Mod-01 Lec-28 Functions of Multiple Random Variables (Contd...2).
Mod-01 Lec-29 Introduction to Copulas.
Mod-01 Lec-30 Introduction to Copulas (Contd.).
Mod-01 Lec-31 Probability Models using Normal Distribution.
Mod-01 Lec-32 Probability Models using Log Normal and Exponential Distribution.
Mod-01 Lec-33 Probability Models using Gamma and Extreme Value Distribution.
Mod-01 Lec-34 Probability Models using Discrete Probability Distributions.
Mod-01 Lec-35 Sampling Distribution and Parameter Estimation.
Mod-01 Lec-36 Sampling Distribution and Parameter Estimation (Contd.).
Mod-01 Lec-37 Hypothesis Testing.
Mod-01 Lec-38 Goodness - of - fit tests.
Mod-01 Lec-39 Regression Analyses and Correlation.
Mod-01 Lec-40 Regression Analyses and Correlation (Contd.).

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