Some mathematics concepts are required to be understood by a statistician or data scientist to learn the subject of statistics more effectively. In many courses of statistics, you apply functions to perform some tasks of interest. So, the first two units of this course are devoted to explaining different terms related to function. Summation and integration both are used in statistics. So, it becomes important to understand what actually they do, especially integration. Unit 5 explains it. Studying concepts in more than two dimensions is required especially in multivariate analysis. The use of vector notations makes the study of multivariate analyse easy. So, a review of vectors and their use in studying some geometric entities like equations of a line, plane and hyperplane are discussed in Unit 6. Change of order of summation and integration is another important idea which is discussed in Unit 9 of this course. Some other useful concepts that are discussed in this course include convergence of sequences and series, and beta and gamma functions. Convexity and concavity of functions are also discussed in this course which will be helpful in understanding optimisation problems.

We use tools and techniques of probability theory to model the uncertainty of a phenomenon. Probability is based on the deep concept of measure theory. In this course, Unit 1 gives an overview of the basic concepts of probability theory studied in earlier classes. But in earlier classes, you did not study actually how probability is assigned to all the events of our interest. Here we will start our study with an explanation of this important concept of how probability is assigned in discrete and continuous worlds. But to do this job we have to apply some concepts of measure theory. So, some of the results of measure theory have been discussed in Units 2 and 3. The next important idea in the world of probability is a random variable. What is a random variable is explained through lots of examples and visualisation of the concepts is also done. To model real-life phenomena, we have discussed some discrete and continuous probability distributions. Finally, this course discusses some important and useful inequalities and laws. Central Limit Theorem has a crucial role in the applications of statistics. Keeping this in view some applications of the Central Limit Theorem are also discussed in this course.

This course is worth four credits and it requires an average of about 120 hours of study time at your end. As is evident from the name of the course, it has been designed to cover the contents from the domains of Sampling Theory, Analysis of Variance and Design of Experiments. The course content has been divided into a total of sixteen units that are organised into four blocks. The first block containing five units cover the topics of Simple Random sampling and PPS sampling. The aim of this block is to highlight and emphasize some concepts and theories mainly related to two fundamental sampling schemes, namely, Simple Random Sampling (SRS) and Probability Proportional to Size (PPS) Sampling, which give rise to many other advanced sampling schemes. The second block containing four units covers the topics of Stratified and Systematic Sampling. In this block, we explain the concept of stratification and allocation of sample size which are made by the researcher purposefully in order to gain some efficiency over the simple random sampling procedure. This block also discusses the Post stratification scheme, This block also deals with another type of sampling scheme which is known as systematic sampling. The third block deals with the applications of ANOVA in various types of data with a number of classification problems of the data and descrbes the concept of ANOVA, its definitions, terminologies used therein and their explanations, mathematical models used in ANOVA with the explanation of underlying parameters and assumptions in each model on the basis of which the mathematical treatment of ANOVA is possible and various uses of ANOVA. The remaining fourth block containing three units covers topics of Design of Experiments. It also deals with the study and applications of Completely Randomised Design when we come across with the analysis problem of such data which are available in the one-way classified form. This block discusses the application of Randomised Block Design for testing the equality of several population means for two-way classified data, assuming that during the process of division of data, each cell consists of only one observation. The Latin Square Design where the experimenter wishes to analyze the two-way classified data but with more than one observation in each cell also discussed in this block.

The aim of this course is to develop the skills of learners to apply the statistical techniques and tools in quality control, time series and reliability. This course is comprised of eighteen units that are organised into four blocks into two volumes. The first block describes the concepts of quality control and the methods of process control by using the different kinds of quality control charts for variables as well as for attributes along with the control charts for small shifts. This block has an additional unit to describe the concept of process capability and six-sigma. The second block is devoted to describing the use of statistical tools for second part of quality control, that is, product control. We explain what acceptance and rectifying sampling plans are and how these implement in the industry to control the quality of the products. We also discuss the single and double sampling plans for attributes. We describe various features of both sampling plans, such as operating characteristic (OC) curve, average outgoing quality (AOQ), producer’s risk, consumer’s risk, average sample number (ASN), average total inspection (ATI) and how to design these plans. The aim of the third block is to introduce and explain basic methods for analysis of time series. Time series analysis is the art of extracting meaningful insights and revealing patterns from time series data using statistical and data visualization approaches. We start with what is time series? and what are its components, various techniques of estimating trend and seasonal effects, some fundamental concepts that are necessary for a proper understanding of time series modelling such as stationarity, non-stationarity, and correlation analysis in time series also discussed. We explain various time series models which are used for stationary time series such as autoregressive model, moving average model, autoregressive moving average model and autoregressive integrated moving average model used for nonstationary time series. In the fourth block, we explain another important topic reliability theory. Reliability means of a component/system means how long it performs its intended function successfully under given conditions. Here, we explain various basic functions of reliability, and reliability evaluation of simple and complex systems.

This course is designed to acquaint the learners with the basic data structure and fundamentals of coding concepts in R language. The content of the course will help the learners to develop essential computing skills. These computing skills will help the learners to apply statistical techniques using R Software. This is a compulsory core theory course of 2 credits. This course will help the learners throughout the MSCAST programme, to transform theory into practice. It comprises details on vectors, list, data frames, matrices, arrays, factors, testing and coercion commands, reading and writing data in R, graphical representation of data, control structure, functions and loop functions, etc. Learners will also learn to do descriptive statistics analysis and correlation analysis using R with the help of this course.

The purpose of introducing this course is to understand some useful techniques of statistics to draw inferences about the population on the basis of sample(s). This course is comprised of seventeen units that are organised into four blocks and two blocks into one volume. In the first block, we describe the basic concepts and methodologies of sampling distributions of various statistics. Here, we also discuss some important sampling distributions which are widely used in statistical inference and known as exact sampling distributions such as Chi-square, t and F distributions with their applications. Broadly, statistical inference is divided into two parts: Estimation and Testing of hypothesis. The population parameters are generally unknown, and we may want to guess the true value of the unknown parameters on the basis of a random sample drawn from the population. This type of problem is known as “Estimation”. Estimation admits two problems; the first is to select some criteria or properties such that if an estimator possesses these properties it is said to be the best estimator among all possible estimators and the second is to derive some methods or techniques through which we obtain an estimator which possesses such properties. The second block explains the first part, that is, properties of good estimators such as unbiasedness, consistency, efficiency, and sufficiency with different examples whereas the third block explores the basic concepts and methods of interval estimation. In the fourth block, the second part of statistical inference, that is, testing of hypothesis, is discussed. We discuss how a hypothetical value of the population parameter can be tested and how we can take the decision about the rejection or non-rejection of the hypothesis or assumed value. Here, different parametric tests as Z-test, t-test, F-test and Chi-square test for testing of hypothesis about population mean, difference of two population means, population proportion, difference of two population proportions, population variance, etc. are also discussed.

This course is designed to develop the skills of performing regression analysis, which is one of the most widely used methods for studying the dependence of one dependent (response) variable on one or more independent (explanatory) variables. The course content has been divided into units that are organised into four blocks and two blocks into one volume. It is a compulsory core course of the programme worth four credits. The course explains the fitting and related analysis of Simple and Multiple Linear Regression Models, Residual Analysis, Autocorrelation, Partial Regression and Partial Residual Plots, Transformations, Polynomial Models, Diagnostic for Leverage and Influence Points, Multicollinearity, Heteroscedasticity, Autocorrelation, Variable Selection and Model Building. It also discusses the Generalised Linear Model, which covers the Logistic Regression Models, Linear Predictor and Link Functions, Maximum Likelihood Estimation of Parameters, Probit Model, Complementary Log-Log Model, Multinomial Logistic Regression Models, Poisson Regression Models, Exponential Family of Distribution, Linear Predictors and Link Functions.

This course is specially designed to develop the understanding of the multivariate data and multivariate techniques. To make the learners acquire these multivariate concepts, the content of the course ranging from some basic standard Matrix Algebra and Linear Algebra results to complex concepts such as multivariate distributions, Multivariate normal distribution and multivariate statistical techniques. In this course, learner will develop the understanding and learn some most useful multivariate techniques such as Principal Component Analysis, Factor Analysis, Cluster Analysis, Discriminant Analysis, Classification, Canonical correlation, one-way MANOVA. In addition to this, the learners will also learn Wishart distribution, Hotelling’s T² statistic, Mahalanobis D² statistic etc. This is a compulsory core theory course of 4 credits of the programme.

The nature of the programme is applied so in this course you will study applications of statistics in two areas namely Epidemiology and Clinical Trials. Thus, this course is divided into two blocks where Block 1 is devoted to epidemiology and Block 2 is devoted to Clinical trials. Block on epidemiology explains what epidemiology is, and what types of studies are done by epidemiologists. The distinction between descriptive and analytic epidemiology is explained. Different study designs which are generally used to conduct epidemiological studies are discussed together with their data analysis. The screening programme and evaluation of the screening programme are also discussed.

This course is worth four credits and it is offered in the third semester of the M.Sc.(Applied Statistics) programme. This course has been designed to cover the advance sampling schemes and designs from the domains of Sampling Theory and Design of Experiments. The course content has been divided into a total of sixteen units that are organised into four blocks. The first block containing four units cover the topics of Ratio, Product and Regression Methods of Estimation and Double sampling. The aim of this block is to highlight and emphasize some concepts and theories mainly related to methods of estimation using auxiliary information along with the estimation of their population mean and variance of the estimator. The comparative study with respect to the simple random sampling has also been provided in this block. The second block containing four units covers the topics of Cluster and Two-stage Sampling along with the estimation of their population mean and variance of the estimator. The Randomised Response technique has also been discussed in this block. The third block deals with the topics related to Factorial Experiments and Fractional Factorial experiments. A Brief review of Design and Analysis of 22, 23 and 2n Factorial experiments has been presented in this block. The Design and Analysis of 32 and 33 Factorial experiments along with their uses and concepts have been described in this block. The remaining fourth block containing four units covers topics of Incomplete Block Designs and Split Plot design. It also deals with the Confounding in 23 experiments, Partial confounding, and its analysis. This block discusses the different concepts and analysis of the Balanced Incomplete Block Design (BIBD). The Parameters and analysis of Split plot design and Response surface design. also discussed in this block.

The aim of this course is to develop the skills to describe advanced classical and Bayesian estimation with generation of random numbers from different distributions. The first block of this course is devoted to explaining uniformly minimum variance unbiased estimators with fisher information, Cramer-Rao inequality, Rao-Blackwell and Lehman-Scheffe theorems. In the second block is devoted to explaining the derivation of a test for testing a hypothesis using Neyman-Pearson's lemma, likelihood ratio test and also discuss the Wald’s fundamental identity. The course MST-016 is based on parametric tests but in many real-life problems particularly in social and behavioural sciences, neither one can know the form of population, nor the observations measured in quantitative form. In such situations, the parametric tests are not applicable. Thus, in the third block of this course, we discuss various nonparametric tests such as one-sample tests, two-sample tests, k-sample tests and analysis of frequencies. Block fourth of this course explains the concept of Bayesian approach. Various forms of loss functions and techniques of Bayesian estimation are also discussed in this block with generation of random numbers from various discrete and continuous distributions.

In statistics, we have data on different variables. In the introduction of the course MST-011 we have said that the use of vector notations makes the study of multivariate analyse easy. To study vectors in n dimension and operations on vectors we need to develop a structure of vectors. The name of branch of mathematics where we study to perform different operations on a structure of vectors is known as linear algebra. The first two blocks of this course are devoted to explaining tools and techniques of linear algebra which will later help us to study multivariate analysis as well as machine learning algorithms. To study optimisation problems in the n dimension, we need to understand multivariate calculus well. The last two blocks of this course are devoted to explaining different concepts of multivariate calculus. So, this course discusses the concepts of linear algebra and multivariate calculus through lots of examples. Most of the concepts are visualised so that understanding the underlying concept becomes easy.

Research Methodology in Statistics is one of the important courses in Master of Science in Applied Statistics. To equip the students to undertake any research project, an understanding about the various aspects of research and research methodology is very essential. There are introductions to Research, Objectives, types, Research Approach, Significance of Research, Research Methods versus, Methodology, Research Process, Criteria of Good Research Identifying and Formulating research, Problem design, Meaning of Research Design and its need, Features of a Good Design, Concepts relating to research design, Different research design, Literature overview and Patents. [History of Statistics, Mode of Literature Survey-Books and Monographs, Journals, Conference Proceedings, Patents, writing a Research Proposal, Introduction; types; elements of a proposal; steps; do’s and don’ts, Managing Research Project, Overview on how to manage project/dissertation, Funding agencies, do’s and don’ts, Managing References, Managing references using Google Scholar and by using bibliographic software: Zotero. Overview of data considerations, sources of data, selecting appropriate data and methods, Overview of data processing and interpretation, Field Surveys and Validation, Overview of validation, methods, selecting appropriate method, Communication and Presentation, Presenting the research Paper or research proposal, do’s and don’ts, Introduction, selecting suitable journal/platform, journal impact factor, citation index, formatting, acknowledgement and attributions, dos and don’ts, Writing Thesis/Project Report/Technical Note, Introduction, elements, types, do’s and don’ts, Research Ethics, Introduction, responsibility and accountability; ethical considerations; plagiarism, use of plagiarism detection software.

This course aims to teach Python programming, starting from the essential concepts needed for composing a program and moving towards applications related to applied statistics. This course is designed to bring theoretical concepts of Python programming to fruition as an intuitive approach for applications of statistical tools. This course contains several units divided into two blocks. It is a compulsory core course of the programme worth two credits. This course includes Introduction to Python: Integrated Development Environments of Python, Python's Modules; Packages and Libraries, Data Types, Mathematical Operations, Expressions and Statements, Operators, Conditional Statements, Data Visualisation, and Statistical Analysis with Python.

This course is designed to develop the skills of performing categorical and survival analysis. This course contains several units divided into two blocks. It is a compulsory core course of the programme worth two credits and organised into one volume. It includes various statistical tests related to (2x2) and (r x c) Contingency Tables, Measures of Agreement and Disagreement, Sensitivity, Specificity, PPV, NPV, Likelihood-Ratio Test, ROC Curve, Odds Ratio and Relative Risk. It also discusses the basic concept of Survival Analysis, Censored Data, Descriptive Measures of Survival functions, Kaplan-Meier Estimator of Survival Function, Mantel-Haenszel and Log-Rank Tests, Cox PH Model.

Nowadays computers are not only used to do computational work. But computers can be trained to learn from past experience and make decisions. This course discusses some machine learning algorithms which work behind the learning of computers from past experience. You know that statistical learning broadly can be divided into two categories regression and classification. Similarly, machine learning is also categorised broadly into three categories supervised, unsupervised and reinforcement learning. The first two blocks of this course are devoted to discussing these types of machine learning. To search for some content of your interest online you type some keywords on google. To search the content of your interest Google search engine works behind the sense. Google search engine is a well-known neural network. The last two blocks of this course are devoted to discussing the concept of neural networks.

This course discusses the concepts and techniques of operational research, such as the linear programming problem, the simplex method of solving linear programming problems, Revised Simplex Method, Sensitivity Analysis and Duality in LPP, transportation problem, assignment problem, Rectangular Games with Saddle Point, Rectangular Games without Saddle Point, Sequencing problems, Replacement problems, Decision making problems, Dynamic Programming, Deterministic inventory Models, Probabilistic Inventory Models, Poisson Queueing Systems and Non-Poisson Queueing Systems.

This course has been designed to cover the concepts and theories of Markov Chain, Poisson and Wiener Processes, Non-Markovian Stochastic Processes and Applications of Stochastic Processes. The course content has been divided into a total of sixteen units that are organised into four blocks. The first block containing four units covers the topics of introductory basic concepts of stochastic process, theories and methods of Markov Chain, Some Advanced Topics in Markov Chain and Random Walk Model. The second block containing four units covers the topics of Gambler’s Ruin Problem, Poisson Process along with the Generalized form of Poisson Process. The Wiener process, which is a Continuous Stochastic Process has also been discussed in this block. The third block deals with the Non-Markovian Stochastic Processes. The theories and concepts of the Renewal Processes and Branching Process have been discussed in this block. This block also covers the topics of the Stationary Processes and Time Series models along with the Martingales Theory. The remaining fourth block containing four units covers topics of Applications of stochastic processes in Waiting Line Theory like concepts of queueing systems; distributions of arrivals, departures and inter-arrival times and Birth and death process and its application in queueing theory. The Application in G.M. Counter Theory and Stochastic Epidemic Models have also been discussed in this block.