# Mov Probability Models using Discrete Probability Distributions

Sumit Sep 2, 2013 By: Prof. Rajib Maity

**Reads:** 127

**Last modified:** 03 May 2013

**Organization:** IIT Kharagpur

Lecture Details :

Lecture -34 Introduction - Probability Models using Discrete Probability Distributionsof 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 Discrete Probability Distributions; 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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