# Mov Probability Models using Gamma and Extreme Value Distribution

Sumit Oct 10, 2013 By: Prof. Rajib Maity

**Reads:** 131

**Last modified:** 03 May 2013

**Organization:** IIT Kharagpur

Lecture Details :

Lecture -33 Introduction - Probability Models using Gamma and Extreme Value Distribution of Probability Methods in Civil Engineering by Prof. Rajib Maity, Department of Civil Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Detail:

Introduction : Probability Models using Gamma and Extreme Value Distribution; 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, Poissonï¿½s 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.

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