Probability Methods in Civil Engineering

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3 STUDENTS

Contents:
Introduction : Role of Probability in Civil Engineering Problems; Examples.
Random Events : Definition of basic random events; Application of set theory in definition of composite event operations;
Probability of events and definition of probability axioms; Solution of real life examples from civil engineering.
Random Variables : Definition of random variables – discrete and continuous;Probability definitions – PMF, PDF, CDF;Moments and expectations.

Functions of Random Variables : Definition of probability distributions of functions of single random variables – exact methods and approximate methods;Moments and expectations of functions – direct and indirect methods.
Multiple Random Variables : Definition of joint, marginal, and conditional probability distributions;Definitions of moments and expectations, including the definition of correlation coefficient;Functions of multiple random variables.

Common Probability Models : Discrete random variables – binomial distribution, Poisson’s distribution;
Continuous random variables – exponential distribution, gamma distribution;
Central limit theorem; Normal and lognormal distributions; Extremal distributions.

Statistics and sampling : Goodness of fit tests; regression and correlation analyses; estimation of distribution parameters from statistics;
Hypothesis testing and significance; Bayesian updating of distributions.

Course Curriculum

Mod-01 Lec-01 Introduction – Role of Probability in Civil Engineering Details 54:1
Mod-01 Lec-02 Random Events and Probability Concept Details 53:44
Mod-01 Lec-03 Set Theory and Set Operations Details 49:50
Mod-01 Lec-04 Axioms of Probability Details 49:6
Mod-01 Lec-05 Probability of Events Details 53:55
Mod-01 Lec-06 Concept and Defination of Random Variables Details 52:42
Mod-01 Lec-07 Probability Distribution of Random Variables Details 54:38
Mod-01 Lec-08 CDF and Descriptors of Random Variables Details 54:43
Mod-01 Lec-09 Further Descriptors of Random Variables Details 55:29
Mod-01 Lec-10 Discrete Probability Distribution Details 55:4
Mod-01 Lec-11 Probability Distribution of Continuous RVs Details 57:23
Mod-01 Lec-12 Probability Distribution of Continuous RVs (Contd…1) Details 54:45
Mod-01 Lec-13 Probability Distribution of Continuous RVs (Contd…2) Details 56:41
Mod-01 Lec-14 Functions of Single Random Variables Details 53:34
Mod-01 Lec-15 Functions of Random Variables – Different Methods Details 53:55
Mod-01 Lec-16 Functions of Random Variables – Different Methods (Contd.) Details 55:22
Mod-01 Lec-17 Expectation and Moments of Functions of RV Details 58:25
Mod-01 Lec-18 Expectation and Moments of Functions of RV (Contd.) Details 56:13
Mod-01 Lec-19 Joint Probability Distribution Details 56:30
Mod-01 Lec-20 Marginal Probability Distribution Details 50:9
Mod-01 Lec-21 Conditional Probability Distribution Details 55:43
Mod-01 Lec-22 Conditional Probability Distribution (Contd.) Details 54:2
Mod-01 Lec-23 Properties of Multiple Random Variables Details 55:59
Mod-01 Lec-24 Properties of Multiple Random Variables (Contd.) Details 56:36
Mod-01 Lec-25 MGF of Multivariate RVs and Multivariate Probability Distributions Details 58:16
Mod-01 Lec-26 Multivariate Distribution and Functions of Multiple Random Variables Details 54:12
Mod-01 Lec-27 Functions of Multiple Random Variables (Contd…1) Details 57:25
Mod-01 Lec-28 Functions of Multiple Random Variables (Contd…2) Details 56:26
Mod-01 Lec-29 Introduction to Copulas Details 55:20
Mod-01 Lec-30 Introduction to Copulas (Contd.) Details 52:52
Mod-01 Lec-31 Probability Models using Normal Distribution Details 55:41
Mod-01 Lec-32 Probability Models using Log Normal and Exponential Distribution Details 58:30
Mod-01 Lec-33 Probability Models using Gamma and Extreme Value Distribution Details 57:46
Mod-01 Lec-34 Probability Models using Discrete Probability Distributions Details 59:16
Mod-01 Lec-35 Sampling Distribution and Parameter Estimation Details 54:51
Mod-01 Lec-36 Sampling Distribution and Parameter Estimation (Contd.) Details 57:43
Mod-01 Lec-37 Hypothesis Testing Details 54:43
Mod-01 Lec-38 Goodness – of – fit tests Details 57:14
Mod-01 Lec-39 Regression Analyses and Correlation Details 52:40
Mod-01 Lec-40 Regression Analyses and Correlation (Contd.) Details 54:27

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