About the course
The use of statistical reasoning and methodology is indispensable in modern world. It is applicable to every discipline, be it physical sciences, engineering and technology, economics or social sciences. Much of the advanced research in electronics, electrical, computer science, industrial engineering, biology, genetics, and information science relies increasingly on use of statistical tools. It is essential for the students to get acquainted with the subject of probability and statistics at an early stage. The present course has been designed to introduce the subject to undergraduate/postgraduate students in science and engineering. The course contains a good introduction to each topic and an advance treatment of theory at a fairly understandable level to the students at this stage. Each concept has been explained through examples and application oriented problems.
Pre-requisites
Must have good knowledge of Differential and Integral Calculus, sequences and series, Basic Linear/Matrix Algebra (usually students who have completed Mathematics-I and II at first year undergraduate
Industries that will recognize this course
Today all industries use statistical methods. So for students desirous to work in any type of industry, this course will be indispensable. In particular, companies dealing with Business Analytics, Banking and finance, Insurance machine learning, data mining etc. this course will be invaluable.
INTERNSHIP/JOB OPPORTUNITIES FOR TOP 5% OF THIS COURSE AT VuNet:
VuNet Systems( www.vunetsystems.com ) brings in a big data approach to manage the complex IT infrastructure of enterprises. With its powerful analytics and intuitive visualisations, it helps connect the 1000s of dots in an IT infrastructure to keep it always on and secure. VuNet has customers across verticals, from banks, manufacturing, consumer care to IT/ITES, with some leading retail payment companies as well. VuNet has also been recognised among the NASSCOM Emerge50 innovative product startups and is also part of the Cisco Launchpad program - Cisco’s partnership program with top emerging startups.
We are always on the lookout for talented programmers and will interview the course toppers( top 5% ), who are interested in an internship/job opportunity. Upon completion of this course, the toppers can submit their resumes and programming code samples. VuNet will interview the candidates and offer internships or job opportunities based on the interview.
Course
instructor 
Somesh Kumar is a professor in the Department of Mathematics, IIT Kharagpur. He has over 28 years of experience of teaching courses on Probability Statistics, Statistical Inference, Sampling Theory, Stochastic Processes, Multivariate Analysis, Regression analysis, Time Series, Experimental Designs, Decision Theory to undergraduate, postgraduate and doctorate students. His NPTEL courses (under MHRD) on Probability and Statistics, Statistical Inference and Statistical Methods for Scientists and Engineers (each of 40 hours) are available online. He has also taught Mathematics-I in QEEE program of MHRD to 130 engineering college students in online mode during Autumn 2014-2015. He offered this course “Probability and Statistics” for certification program in Jan-April 2016.
His research interests are Statistical Decision Theory, Estimation Theory, Classification Problems, Directional Distributions, Limit Theorems. He has published more than 70 research papers in reputed international journals. He has supervised eight doctoral and more than a hundred and fifty Masters (M.Tech. and M.Sc.) dissertations.
Course layout
Week 1: Sets, Classes, Collections
Sequence of Sets
Ring, Field (Algebra)
Sigma-Ring, Sigma-Field, Monotone Class
Random Experiment, Events
Definitions of Probability
Properties of Probability Function-I
Properties of Probability Function-II
Week 2: Conditional Probability
Independence of Events
Problems in Probability-I
Problems in Probability-II
Random Variables
Probability Distribution of a Random Variable-I
Week 3: Probability Distribution of a Random Variable-II
Moments
Characteristics of Distributions-I
Characteristics of Distributions-II
Special Discrete Distributions-I
Special Discrete Distributions-II
Special Discrete Distributions-III
Week 4: Poisson Process-I
Poisson Process-II
Special Continuous Distributions-I
Special Continuous Distributions-II
Special Continuous Distributions-III
Special Continuous Distributions-IV
Special Continuous Distributions-V
Week 5: Normal Distribution
Problems on Normal Distribution
Problems on Special Distributions-I
Problems on Special Distributions-II
Function of a Random Variable-I
Function of a Random Variable-II
Week 6: Joint Distributions-I
Joint Distributions-II
Independence, Product Moments
Linearity Property of Correlation and Examples
Bivariate Normal Distribution-I
Bivariate Normal Distribution-II
Week 7: Additive Properties of Distributions-I
Additive Properties of Distributions-II
Transformation of Random Variables
Distribution of Order Statistics
Basic Concepts
Chi-Square Distribution
Week 8: Chi-Square Distribution
(Cont…), t-Distribution
F-Distribution
Descriptive Statistics – I
Descriptive Statistics - II
Descriptive Statistics – III
Descriptive Statistics – IV
Week 9: Introduction to Estimation
Unbiased and Consistent Estimators
LSE, MME
Examples on MME, MLE
Examples on MLE-I
Examples on MLE-II, MSE
Week 10: UMVUE, Sufficiency, Completeness
Rao-Blackwell Theorem and its Applications
Confidence Intervals-I
Confidence Intervals- II
Confidence Intervals- III
Confidence Intervals- IV
Week 11: Basic Definitions
Two Types of Errors
Neyman-Pearson Fundamental Lemma
Applications of N-P Lemma-I
Applications of N-P Lemma-II
Week 12: Testing for Normal Mean
Testing for Normal Variance
Large Sample Test for Variance and Two Sample Problem
Paired t-Test
Examples
Week 13: Testing Equality of Proportions
Chi-Square Test for Goodness Fit -I
Chi-Square Test for Goodness Fit –II
Testing
for Independence in 
Contingency Table –I
Testing
for Independence in Contingency Table-II
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