Module 7: Probability and Statistics
Lecture 5: Regression Analyses and Correlation
1. Introduction
This lecture presents the theory and formulations of linear regression with constant and non
constant variances. It also introduces multiple linear regress
Module 6: Common Probability Models
Lecture 2: Probability Models using Log Normal and Exponential Distribution
1. Introduction
The previous lecture dealt with the pdf of Normal distribution, the normal curve and
probability calculation using Standard Nor
Module 6: Common Probability Models
Lecture 3: Probability Models using Gamma and Extreme Value Distribution
1. Introduction
In the previous lecture, discussions on Lognormal and Exponential distribution were
presented. In this chapter, the pdf of Gamma d
M5L12
Introduction to Copulas-2
1. Introduction
This is the second lecture on copula function. We have discussed on the definition of copula
function with explanation, its properties, basic terminologies, Sklar theorem etc. in the
previous lecture. Here a
M5L9
Functions of Multiple Random Variables-2
1. Introduction
In this lecture, various statistical properties of one function of two random variables are
discussed. The sum and difference of independent Normal variates, maximum, minimum
product and quotie
M5L8
Multivariate Distribution and Functions of Multiple Random Variables
1. Introduction
In this lecture, marginal and conditional probability distributions for multivariate RVs,
functions of multiple random variables, single function for two random vari
M5L7
Moment Generating Function of Multivariate RVs and Multivariate
Probability Distributions
1. Introduction
In this lecture, moment generating functions, bivariate probability distribution function and
joint probability of multivariate random variables
M5L5
Properties of Multiple Random Variables
1. Introduction
As mentioned in previous lecture, the important measures to explain the properties of
multiple RVs are: moments, covariance, correlation coefficient, conditional mean,
conditional variance, mome
M5L6
Properties of Multiple Random Variables-2
1. Introduction
This is the second part of lecture on properties of multiple random variables. There are a few
measures important to discuss in the context of multiple RVs. Among these measures,
moments, cova
M5L11
Introduction to Copulas
1. Introduction
In this lecture, the theory of copula is introduced. The definition of copula function with
explanation, its properties, basic terminologies, Frchet-Hoeffding Bounds, Sklar theorem
and measures of dependence a
Module 6: Common Probability Models
Lecture 1: Probability Models using Normal Distribution
1. Introduction
This module introduces some common probability models which find widespread application
in Civil Engineering. This lecture deals with the probabili
NPTEL Syllabus
Probability Methods in Civil Engineering - Web
course
COURSE OUTLINE
NPTEL
Concept of probability and statistics is very important to solve various civil engineering
problems. In this video course, basic probability concept and different pr
Module 7: Probability and Statistics
Lecture 6: Regression Analyses and Correlationcontd.
1. Introduction
In the previous lecture, formulations and problems on linear regression were discussed. The
basic formulation of multiple linear regression was also
Module 7: Probability and Statistics
Lecture 4: Goodness of fit tests
1. Introduction
In the previous two lectures, the concepts, steps and applications of Hypotheses testing were
discussed. Hypotheses testing may be used to check the validity of a hypoth
Module 7: Probability and Statistics
Lecture 3: Hypothesis Testing
1. Introduction
In the previous lecture, Hypothesis testing was introduced and the various types of sampling
errors were discussed. This lecture deals with inferences concerning one and tw
Module 7: Probability and Statistics
Lecture 1: Sampling Distribution and Parameter Estimation
1. Introduction
This lecture deals with Sampling distribution and Estimation of parameters. Random
sampling and Point estimation, desirable properties of point
Module 6: Common Probability Models
Lecture 4: Probability Models using Discrete Probability Distributions
1. Introduction
While the preceding three lectures of this module dealt with continuous probability models,
discrete probability models are the subj
Module 7: Probability and Statistics
Lecture 1: Sampling Distribution and Parameter Estimation contd.
1. Introduction
In the previous lecture, Sampling distribution, Point estimation and Interval estimation for
various statistics were discussed. In this l
M5L10
Functions of Multiple Random Variables-3
1. Introduction
So far in this module, the details about one function of two random variables are discussed.
However, there may exist more than one function for two random variables. In this lecture,
two func
M5L4
Conditional Probability Distribution 2
1. Introduction
This is continuation of last lecture on conditional probability distribution. Here conditional
probability distribution is of continuous bivariate random variables and independent random
variable
M4L5
Expectation and Moments of Functions of Random Variable
1. Introduction
This lecture is a continuation of previous lecture, elaborating expectations, moments and
moment generating functions of the functions of random variable discussed earlier.
2. Mo
Module 5: Multiple Random Variables
Lecture 3 Conditional Probability Distribution
1. Introduction
In the previous lecture, marginal probability distribution of jointly distributed RVs was
presented along with suitable example problems. This lecture prese
Module 3: Random Variables
Lecture 5: Some Standard Discrete Probability Distributions
Discrete Random Variables
A discrete random variable is a function that can take only a finite number of values. The
Probability Density Function of a discrete RV indic
M2L4
Probability of Events
1. Introduction
In this lecture, details of various concepts related to probability of events, such as, equality of
events, concept of field, countable and non-countable space, conditional probability, total
probability, Bayes T
M2L3
Axioms of Probability
1. Introduction
This lecture is a continuation of discussion on random events that started with definition of
various terms related to Set Theory and event operations in previous lecture. Details of
axioms of probability, their
Module 3: Random Variables
Lecture 2: Probability Distribution of Random Variables
Probability Distribution of a Random variable
Probability distribution of a Random Variable (RV) is a function that provides a complete
description of all possible values t
Module 3: Random Variables
Lecture 3: CDF and Descriptors of Random Variables
Cumulative Distribution Functions (CDF)
For a discrete or continuous random variable, the Cumulative Distribution Function, abbreviated
as CDF and denoted by Fx(x), is the nonex
M3L1
Concept and Definitions of Random Variables
1. Introduction
This is the first lecture on random variables. In this lecture, the basic concept of random
variable, its definition, different types of random variables, their probability distribution and
M2L2
Set Theory and Event Operations
1. Introduction
This lecture is a continuation of discussion on random events that started with definition of
various terms related to random events and concepts of probability in previous lecture. Here
Set Theory, its
M2L1
Random Events and Probability Concept
1. Introduction
In this lecture, discussion on various basic properties of random variables and definitions of
different terms used in probability theory and its concept are explained.
2. Random Experiment
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