# Descriptive Statistics & Data Analysis

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# Code(Credit) : CUNT2484 (3-0-1)

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.
1. Sheldon Ross, Introduction to Probability Models, 9th Ed., Academic Press, Indian Reprint, 2007.
2. 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

Session-5:

Marginal and conditional distributions

Session-6:

Standard discrete and continuous univariate distributions

Session-7:

Sampling distributions

Session-8:

Standard errors

Session-9:

Asymptotic distributions

Session-10:

Distributions of order statistics and range

Session-11:

Simple non-parametric tests for one sample problem

Session-12:

Simple non-parametric tests for two sample problems

Session-13:

Introduction to Rank Correlation

Session-14:

Problems on Rank correlation

Session-15:

Test for the independence of parameters

Session-16:

Analysis of variance and covariance

Session-17:

Fixed, random and mixed effects models

Session-18:

Simple linear regression

Session-19:

Multiple linear regression

Session-20:

Logistic regression

Session-21:

Multivariate normal distribution

Session-22:

Introduction to Wishart distribution

Session-23:

Properties of Wishart distribution

Session-24:

Session-25:

Inference for parameters

Session-26:

Introduction to data reduction techniques

Session-27:

Introduction to principal component analysis

Session-28:

Application and working principle of principal component analysis

Session-29:

Introduction to discriminant analysis

Session-30:

Introduction to cluster analysis

Session-31:

Simple random sampling

Session-32:

Stratified sampling

Session-33:

Clustering sampling

Session-34: Systematic sampling

Session-35:

Probability proportional to size sampling

## Session

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## Case Studies

### Dr. Mohammed Siddique

##### Asst. Prof. Department of Mathematics
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Dr. Mohammed Siddique, received Ph. D in Mathematics in the area of Optimization Techniques and Machine Learning from KIIT, Deemed to be University, Bhubaneswar and completed his M.Sc in Mathematics and M.Tech in Computer Science from Utkal University, Bhubaneswar.  He is having more than 16 years of teaching experience. He is having more than 50 […]