Objectives

The primary objective of this course is to familiarize students with the fundamental concepts and techniques of probability theory and statistical analysis. The main objective of this course is to provide mathematical concepts and build up strong mathematical fundamentals to support many subjects of computer science engineering. To achieve a good score in the NET examination.

Course Outcomes

COs	Course outcomes	Mapping Cos with POs (High-3, Medium-2, Low-1)
CO1	Can achieve the concepts of sampling which can apply to business decision	PO1(3), PO9(2)
CO2	Can apply the concepts of discrete and continuous probability distributions to make the prediction to the real-life application	PO4(3), PO2(2),
CO5	Compute probabilities based on practical situations using the Binomial, Poisson and Normal distributions.	PO5(2), PO9(2)

Course Syllabus

Module:1

Random variables and distributions functions (univariate and multivariate); Expectations and moments.Marginal and conditional distributions. Characteristic functions.

Module:2                         

Standard discrete and continuous univariate distributions.Sampling distributions, Standard errors, and asymptotic distributions, Distributions of order statistics and range.

Module:3

Simple non-parametric tests for one and two sample problems, Rank correlation, and test for independence.

Module:4

Analysis of variance and covariance. Fixed, random and mixed effects models. Simple and multiple linear regression, Logistic regression.

Module:5

Multivariate normal distribution, Wishart distribution, and their properties. Distributions of quadratic forms. Inference for parameters.

Module:6

Data reduction techniques: Principle component analysis, Discriminant analysis, Cluster analysis.

Module:7

Simple random sampling, stratified sampling, and systematic sampling. Probability is proportional to size sampling.

Projects:

1. Prepare a report on Gauss Markov models
2. Prepare a report on correlation and regression analysis

Text Book:   

1. Irwin Miller and Marylees Miller, John E. Freund, Mathematical Statistics with Applications, 7th Ed., Pearson Education, Asia, 2006.

2. Sheldon Ross, Introduction to Probability Models, 9th Ed., Academic Press, Indian Reprint, 2007.
3. Devore, J. L.: Probability & Statistics for Engineering and the Sciences, 8th edition, Cengage Learning, 2012.

Reference Book:

1. Milton, J. S. and Arnold J. C.: Introduction to Probability and Statistics: Principles andApplicationsforEngineering and theComputing Sciences, 4th edition, TataMcGraw-Hill, 2007.
2. Johnson, R. A., Miller: Freund’s Probability and Statistics for Engineers, 8th edition, PHI, 2010.
3. Meyer, P.L.: Introductory Probability and Statistical Applications, 2ndedition, Addison-Wesley, 1970.
4. Ross, S. M.: Introduction to Probability Models, 11th edition, Academic Press, 2014.

Session Plan

Session-1:

 

Introduction to Random Variables

 

https://in.video.search.yahoo.com/search/video?fr=mcafee&ei=UTF-8&p=Introduction+to+Random+variables&vm=r&type=E210IN714G0#id=0&vid=e878bfaa6a2d0dec8ce0b504175d7016&action=click

 

Session-2:

 

Univariate distribution’s function

 

https://in.video.search.yahoo.com/search/video?fr=mcafee&ei=UTF-8&p=What+is+a+univariate+distribution+in+statistics%3F&type=E210IN714G0#id=2&vid=eb412c34f71af2d2408462604dcd49bb&action=click

 

Session-3:

 

Multivariate distribution’s function

 

https://in.video.search.yahoo.com/search/video?fr=mcafee&ei=UTF-8&p=What+is+a+univariate+distribution+in+statistics%3F&type=E210IN714G0#id=2&vid=eb412c34f71af2d2408462604dcd49bb&action=click

 

Session-4:

 

Expectations and moments

 

https://www.youtube.com/watch?v=H2Ji-Q4MfqU&list=PLU6SqdYcYsfIaokdZTmptaf-PK7s-B0ju&index=4

 

Session-5:

 

Marginal and conditional distributions

 

https://www.youtube.com/watch?v=L0zWnBrjhng

 

Session-6:

 

Standard discrete and continuous univariate distributions

 

https://www.youtube.com/watch?v=Ag8XJuskG78&list=PLRNL7AjA6rjxW80He0tS0Xv1l2PEvAQNZ

 

Session-7:

 

Sampling distributions

 

https://www.youtube.com/watch?v=z0Ry_3_qhDw

 

Session-8:

 

Standard errors

 

https://www.youtube.com/watch?v=4kDScWSaEWs

 

Session-9:

 

Asymptotic distributions

 

https://www.youtube.com/watch?v=Za1YxRJL-SA&list=PLwJRxp3blEvZBAn3bwAAtdJqotRPBWBlP

 

Session-10:

 

Distributions of order statistics and range

 

https://www.youtube.com/watch?v=pJh1oZ401NI

 

Session-11:

 

Simple non-parametric tests for one sample problem

 

https://www.youtube.com/watch?v=9vwucf8RZH0

 

Session-12:

 

Simple non-parametric tests for two sample problems

 

https://www.youtube.com/watch?v=Cq9Jr6v8p0M

 

Session-13:

 

Introduction to Rank Correlation

 

https://www.youtube.com/watch?v=E-S-E6HsR_k

 

Session-14:

 

Problems on Rank correlation

 

https://www.youtube.com/watch?v=HdUul6xIocg

 

Session-15:

 

Test for the independence of parameters

 

https://www.youtube.com/watch?v=y5nxiL6civU

 

Session-16:

 

Analysis of variance and covariance

 

https://www.youtube.com/watch?v=UwzuJW4P2Jw

 

Session-17:

 

Fixed, random and mixed effects models

 

https://www.youtube.com/watch?v=8e0zaHhTHyY

 

Session-18:

 

Simple linear regression

 

https://www.youtube.com/watch?v=lzGKRSvs5HM

 

Session-19:

 

Multiple linear regression

 

https://www.youtube.com/watch?v=dQNpSa-bq4M

 

Session-20:

 

Logistic regression

 

https://www.youtube.com/watch?v=zAULhNrnuL4

 

Session-21:

 

Multivariate normal distribution

 

https://www.youtube.com/watch?v=UVvuwv-ne1I

 

Session-22:

 

Introduction to Wishart distribution

 

https://www.youtube.com/watch?v=0WY9WYZGl9c

 

Session-23:

 

Properties of Wishart distribution

 

https://www.youtube.com/watch?v=nkTZ7XdIp-A

 

Session-24:

 

Distributions of quadratic forms

 

https://www.youtube.com/watch?v=2J8pVynRZ8A

 

Session-25:

 

Inference for parameters

 

https://www.youtube.com/watch?v=HIiBoL-z0cU&list=PLHRHy1-UoGh2pdh2hqTAUKtb0bCjttby8

 

Session-26:

 

Introduction to data reduction techniques

 

https://www.youtube.com/watch?v=0l3tzQI_ApM

 

Session-27:

 

Introduction to principal component analysis

 

https://www.youtube.com/watch?v=F5DhWBsp8J4

 

Session-28:

 

Application and working principle of principal component analysis

 

https://www.youtube.com/watch?v=osgqQy9Hr8s

 

Session-29:

 

Introduction to discriminant analysis

 

https://www.youtube.com/watch?v=2EjGJXzsC2U

 

Session-30:

 

Introduction to cluster analysis

 

https://www.youtube.com/watch?v=3MnVCX94jJM

 

Session-31:

 

Simple random sampling

 

https://www.youtube.com/watch?v=KLAEwukvuZs

 

Session-32:

 

Stratified sampling

 

https://www.youtube.com/watch?v=O5TjsbZBs2E

 

Session-33:

 

Clustering sampling

 

https://www.youtube.com/watch?v=O5TjsbZBs2E

 

Session-34: Systematic sampling

 

https://www.youtube.com/watch?v=QFoisfSZs8I

 

Session-35:

 

Probability proportional to size sampling

 

https://www.youtube.com/watch?v=nuOtA2TwouU

Session Plan

Session

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Case Studies

Case Studies