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September 26, 2023

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Description

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

Concept of probability and statistics is very important to solve various civil engineering problems. In this course, basic probability concept and different probabilistic models will be discussed. Concept and definition of random variables and different functions of random variables will be covered in the initial part of the course. Afterwards, 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. (from nptel.ac.in)

Course Curriculum

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

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