Available courses

Module
I: Matrices & Determinants                                                   
Module II: Sets, Relations, and Functions             
Module III: Differentiation                                                               
Module IV: Integration                                                                    
Module V: Coordinate Geometry                                                       

Module I: Introduction & Linear Programming Problem.

Module II: Transportation and Assignment problem

Module III: Statistics & Probability Distributions

Module IV: Game theory

Module V: Network Analysis

Module I: Introduction

Module II: Research Design and Research Instruments

Module III: Data Collection, Preparation & Analysis

Module IV: Hypothesis Testing

Module V: Multivariate analysis

Course Contents: 

 Module I: Introduction and Analysis of Univariate data

Module II: Analysis of bivariate data

Module III: Probability

Module IV: Random variables and Probability distributions

Module V: Statistical Inference


Course Contents:

Module I: Collection of data: Classification and Tabulation

Module II: Measures of Central Tendency

Module III: Measures of dispersion

Module IV: Correlation and Regression:

Module V: Probability

Module VI: Random variables and sampling theory


Module I: Non-Linear Equations and System of Linear Equations

Module II: Numerical Integration System of Nonlinear Equations

Module III: Numerical Solution of Ordinary Differential Equations

Module IV: Statistics

Module V: Sampling theory

Module I: Introduction to probability and Linear Programming Problem.

Module II: Transportation and Assignment problem  

Module III: Metaheuristic Optimization Techniques

Module IV: Game theory and Simulation

Module V: Decision theory and Forecasting

Module I: Introduction to statistics

Module II: Correlation regression and fitting of curve

Module III: categorical data analysis

Module IV: Sampling

Module V: hypothesis testing  

Course Contents:
Module I: Introduction                                              
Research & its Methodology: Definitions, Nature, Scope & Types of research, Stating the research problem and developing an approach, Importance of statement of research objectives.
 
Module II: Research Design and Research Instruments                                                
Features of a good research design; Concept and Importance of Research Design: Experimental Design: Concept of Independent & Dependent variables. Comparison on important research designs (Exploratory, Descriptive and Experimental).
 
Module III: Data Collection, Preparation & Analysis                                           
Methods of Data Collection - Observational and Survey Methods, Questionnaire Design. Sampling Methods and Sampling Distributions:  Statistics and Parameter, Sampling distributions - conceptual basis; standard error; sampling from normal populations; relationship between sample size and standard error.
 
Module IV: Hypothesis Testing                              
Null and Alternative Hypotheses; Type I and Type II errors; the significance level. Chi–square and Analysis of Variance: Chi-square as a test of (a) independence and (b) goodness of fit; ANOVA, Non-parametric tests & its applications.
 
Module V: Multivariate analysis                             
Factor Analysis, Multiple Regression Analysis, Multiple Discriminant Analysis and Logistic Regression, Multivariate Analysis of Variance.

 -4201                                                                                           L–T–P–C: 3–0–0– 3        Mathematical Foundation in Data Science                                        

Module

Detailed Contents

Hrs.

01

Linear Algebra

1.1 Vectors and spaces

Vectors, Operations with vectors, Linear combinations and spans, Linear dependence and independence, Norms, Basis, Vector space, Subspaces and the basis for a subspace, Vector dot, cosine and cross products, Matrices for solving systems by elimination, Null space and column space, Modulus & inner product, Projection, Changing basis, Applications of changing basis

1.2 Matrices in Linear Algebra and their transformations

Matrices-vectors and solving simultaneous equation problems, solving linear equations using the inverse matrix, How matrices transform space, Functions and linear transformations, Linear transformation examples, Transformations and matrix multiplication, Inverse functions and transformations, Solving the apples and bananas problem: Gaussian elimination, Going from Gaussian elimination to finding the inverse matrix, Finding inverses and determinants, Determinant depth, Transpose of a matrix. Einstein summation convention and the symmetry of the dot product, Matrices changing basis, Doing a transformation in a changed basis, Orthogonal complements, Orthogonal projections, Orthogonal matrices, The Gram–Schmidt process, Reflecting in a plane

1.3 Eigenvalues and Eigenvectors: Application to Data Problems

What are eigenvalues and eigenvectors, Special eigen-cases, Calculating eigenvectors, Changing to the Eigen basis, Eigenbasis example, Introduction to PageRank, Selecting eigenvectors by inspection, Characteristic polynomials, eigenvalues and eigenvectors, Diagonalization and applications, Eigenvalues and eigenvectors, Matrix Decompositions: Eigen decomposition, Singular Value Decomposition

 

4

 

 



6

 

 

 

 

 

 

5

 

 

02

Multivariate Calculus

2.1 Multivariable functions

Introduction to multivariable calculus, Visualizing scalar-valued functions, Visualizing vector-valued functions, Transformations, Visualizing multivariable functions, Product rule, Chain rule

 2.2 Derivatives of multivariable functions

Partial derivatives, Gradient and directional derivatives, Partial derivative and gradient, Differentiating parametric curves, Multivariable chain rule, Multivariate Chain Rule, Simple Neural Network, Curvature, Partial derivatives of vector-valued functions, Differentiating vector-valued functions, Divergence, Curl, Laplacian, Jacobian, The Sandpit, The Hessian.

2.3 Taylor series and linearization

Building approximate functions, Power series, Power series derivation, Power series details, Linearisation, Multivariate Taylor, Matching functions and approximations. Applying the Taylor series, Taylor series - Special cases, 2D Taylor series

2.4 Applications of multivariable derivatives

Tangent planes and local linearization, Quadratic approximations, Optimizing multivariable functions, Lagrange multipliers and constrained optimization, Gradient Descent, Constrained optimisation, Newton-Raphson in one dimension, Checking Newton-Raphson, Lagrange multipliers

2.5 Regression

Simple linear regression, General non linear least squares, Least squares regression analysis

2.6 Integrating multivariable functions

Line integrals for scalar functions, Line integrals in vector fields, Double integrals, Triple integrals, Surface integral preliminaries, Surface integral, Flux in 3D

2.7 Green's, Stokes', and the divergence theorems

Formal definitions of div and curl, Green's theorem, 2D divergence theorem, Stokes' theorem, 3D divergence theorem, Divergence theorem, Proof of Stokes' theorem, Types of regions in three dimensions, Divergence theorem proof.

3

 

 

 

4

 

 

 


4

 

 

 

4

 

 

3

 

 

3

 

 

3

 Total: 39


UNIT-1 Basic Probability

1.       Probability spaces, Basic terminology

2.       Classical and axiomatic definition and simple rules

3.       Addition theorem (Mutually exclusive or not condition)

4.       Independence and conditional probability,

5.       Bayes' rule

6.       Random variable Discrete random variables and their properties distribution functions

7.       continuous random variable and their properties, distribution functions and densities,

8.       Chebyshev's Inequality,

UNIT-2 Single Random Variables                                                                                         

1.       Expectations, Characteristic functions,

2.       Application exercises to Some special distributions:

3.       Uniform, Binomial, and

4.       Poisson distribution

5.       Exponential, Laplace,

6.       Gaussian.

7.       Functions of single Random Variables,

8.       Conditioned Random variables.

UNIT-3 Multiple Random Variables

1.       Concept, Two variable CDF and PDF,

2.       Two Variable expectations (Correlation, orthogonality, Independent),

3.       Two variable transformation,

4.       Two Gaussian Random variables, Sum of two independent Random Variables,

5.       Sum of IID Random Variables – Central limit Theorem and law of large numbers,

6.       Conditional joint Probabilities,

7.       Application exercises to Chi-square RV, Student-T RV,

8.       Cauchy and Rayleigh RVs.

UNIT-4 Large samples (n > 30)                                                                     

1.       Sampling Distribution of means and variance, Hypothesis Testing: General concepts,

2.       Testing a Statistical hypothesis, one and two-tailed tests, Critical region,

3.       Confidence interval estimation.

4.       Single and two sample tests on proportion.

5.       Single and two sample tests on mean.

6.       Single and two sample tests on variance.

UNIT-5. Small samples (n < 30)

1.       Correlation, lines of regression (two variable only).

2.       Test for single mean, difference of means and

3.       correlation coefficients,

4.       test for ratio of variances F- distribution – Testing of Hypothesis and

5.       independence of attributes,

6.       t-distribution, and Time Series Unit.


BM-3005                                                                                                                         L-T-P-C     

Operation Research                                                                                            4-0-0-4

Pre-requisite

 

Objective: The aim of this course is to acquaint the students with tools & techniques of operations research. Optimization has remained a key challenge for industry since its inception.  This  course  provides  introductory  concepts  of  the  kind  of  optimization problems  industry is confronted with & moves on to more advanced concepts like dynamic programming & games theory.

 

Course outcome: the learner will be able to

 

1.  Understand operations research methodologies

 

2.  Help students to solve various problems practically

 

3.  Make students proficient in case analysis and interpretation

Course content

 

Module01: Introduction to Operations Research and Linear Programming Introduction   To   Operations   Research,   ,   Operations   Research   -   Definition, Characteristics of OR, Models, OR Techniques, Areas of Application, Limitations of OR.,   Linear Programming Problems: Introduction  and Formulation, Introduction to Linear  Programming,  Applications  of  LP,  Components  of  LP,  Requirements  for Formulation of LP Problem, , Assumptions Underlying Linear Programming, , Steps in Solving  LP  Problems,  LPP  Formulation  (Decision  Variables,  Objective  Function, Constraints, Non Negativity Constraints),   Linear Programming Problems: Graphical Method,  ,  Maximization  & Minimization Type Problems. (Max.  Z  & Min.  Z),   Two Decision Variables and Maximum Three Constraints Problem, , Constraints can be “less than or equal to”, “greater than or equal to” or a combination of both the types i.e. mixed  constraints., Concepts:  Feasible  Region  of  Solution,  Unbounded  Solution,

Redundant Constraint, Infeasible Solution, Alternative Optima., Linear Programming Problems: Simplex Method, Only Maximization Type Problems. (Only Max. Z). No Minimization problems. (No Min. Z), Two or Three Decision Variables and Maximum Three Constraints Problem. (Up to Maximum Two Iterations), All Constraints to be “less  than  or  equal  to”  Constraints.  (“Greater  than  or  Equal  to”  Constraints  not included.), Concepts : Slack Variables, Surplus Variables, Artificial Variables, Duality, Product Mix and Profit, Feasible and Infeasible Solution, Unique or Alternate Optimal Solution, Degeneracy, Non Degenerate, Shadow Prices of Resources, Scarce and Abundant  Resources,  Utilized  and  Unutilized  Capacity  of  Resources,  Percentage Utilization of Resources, Decision for Introduction of a New Product.

Module02: Assignment and Transportation Models

 

Assignment   Problem –Hungarian   Method   Maximization & Minimization   Type Problems.  Balanced  and  Unbalanced  Problems.  Prohibited  Assignment  Problems, Unique   or          Multiple   Optimal   Solutions.   Simple   Formulation of   Assignment Problems.Maximum  5  x  5  Matrix.  Up  to  Maximum  Two  Iterations  after  Row  and Column Minimization.

 

Initial Feasible Solution (IFS) by:. North  West  Corner   Rule  (NWCR),  Least   Cost Method (LCM), Vogel’s Approximation Method (VAM), Maximum 5 x 5 Transportation Matrix, Finding Optimal Solution by Modified Distribution (MODI) Method. (u, v and ∆), Maximum Two Iterations (i.e. Maximum Two Loops) after IFS.

Module03: Network Analysis

Critical Path Method (CPM),Concepts: Activity, Event, Network Diagram, Merge Event, Burst Event, Concurrent and Burst Activity,,Construction of a Network Diagram. Node Relationship   and   Precedence   Relationship.,Principles   of   Constructing   N etwork Diagram.,Use  of  Dummy  Activity,Numerical  Consisting  of  Maximum  Ten  (  10) Activities.,Critical Path, Sub-critical Path, Critical  and Non-critical  Activities, Project Completion Time.,Forward Pass  and Backward Pass  Methods.,Calculation of EST, EFT,  LST,  LFT,  Head  Event  Slack,  Tail Event  Slack,  Total  Float,  Free  Float, Independent   Float   and   Interfering   Float,   Project   Crashing,Meaning   of   Project Crashing.,Concepts: Normal Time, Normal Cost, Crash Time, Crash Cost of Activities. Cost Slope of an Activity.,Costs involved in Project Crashing: Direct, Indirect, Penalty and Total Costs.,Time – Cost Trade off in Project Crashing.,Optimal (Minimum) Project Cost and Optimal Project Completion Time.,Process of Project Crashing.,Numerical Consisting of Maximum Ten (10) Activities.,Numerical based on Maximum Four (04) Iterations of Crashing, Program Evaluation and Review Technique (PERT),Three Time Estimates of PERT: Optimistic Time ( Most Likely Time (m) and Pessimistic Time (

.,Expected Time (te) of an Activity Using Three Time Estimates.,Difference between CPM and PERT.,Numerical Consisting of Maximum Ten (10) Activities.,Construction of PERT Network using tevalues of all Activities.,Mean (Expected) Project Completion Time.,Standard  Deviation  and  Variance  of  Activities.,Project  Variance  and  Project Standard Deviation.,‘Prob. Z’ Formula.,Standard Normal Probability Table. Calculation of Probability from the Probability Table using ‘Z’ Value and Simple Questions related to PERT Technique.,Meaning, Objectives, Importance, Scope, RORO/LASH,

 

Module04: Decision Theory, Sequencing and Theory of Games

Decision Theory, Decision Environments – Risk & Uncertainty. Payoff Table, Regret Table,  Decision  Making  under  Uncertainty,  Maximin  &  Maximax  Criteria,  Minimax Regret  Criterion,  Laplace  Criterion,  Hurwicz  Criterion,  Expected  Monetary  Value Criterion, Expected Value of Perfect Information (E.V.P.I), Expected Opportunity Loss (E.O.L).,  Job  Sequencing  Problem,  Processing  Maximum  9  Jobs  through  Two Machines only. Processing Maximum 6 Jobs through Three Machines only. Calculations  of   Idle  Time,  Elapsed  Time  etc.  Theory  of   Games,  Introduction Terminology  of  Game  Theory:  Players,  Strategies,  Play,  Payoff,  Payoff  matrix, Maximin, Maximax, Saddle Point, Types of Games, Numericals based on: Two Person Zero Sum Games, Pure Strategy Games (Saddle Point available)

 

Text/ Reference Books

 

1.   Taha H.A., Operations Research - An Introduction, 6th Edition , Hall of India

2.   Kapoor V.K., Operations Research Techniques for Management, 7th Edition,

Sultan Chand & Sons

3.   Kantiswarup, Gupta P.K. & Manmohan, Operations Research 9th Edition, Sultan

Chand & Sons

4.   Sharma S.D.,Operations Research, 8th Edition, Kedarnath, Ramnath& Company

5.   Bronson R, Operations Research, 2nd Edition, Shaum's Outline Series

6.   Vora N.D, Quantitative Techniques in Management, 3rd Edition, Tata McGraw Hill co.

7.   Shreenath L.S, Principles & Application 3rd Ed,., PERT & CPM, Affiliated East-

West Press Pvt. Ltd.

8.   Wagener H.M.,Principles of Operations Research 2nd Edition, Prentice - Hall of

India

9.   Sasieni M, Yaspan A & John Wiley & Sons Friedman L, Operations Research -

Methods & Problems 1st Edition

10. NatrajanBalasubramani, Tamilarasi, Operations Research, Pearson Education

11. G. Hadley, Linear Programming, Narosa Book Distributors Private Ltd

12. L.C. Jhamb, Quantitative Techniques (For Managerial Decisions VOL I), Everest

Publishing House, Pune.

13. Paul Loomba, Linear Programming, Tata McGraw Hill Publishing Co. Ltd.

14. Aditham B. Rao , Operations Research Edition 2008, Jaico Publishing House,

Mumbai

Course Contents

 

Module 1: Basic Probability (20%)

1.    Probability spaces,

2.    conditional probability, independence;

3.    theorem on probability

4.    Bayes' rule

5.    Discrete random variables, Independent random variables, the multinomial distribution,

6.    infinite sequences of Bernoulli trials, Poisson approximation to the binomial distribution, sums of independent random variables,

7.    Expectation of Discrete Random Variables, Moments, Variance of a sum,

8.    Correlation coefficient, Chebyshev's Inequality.

Module 2: Continuous Probability Distributions(15%)

9.    Continuous random varibales and

10. their properties,

11. distribution functions and densities,

12. normal,

13. exponential and gamma densities

 Module 3: Bivariate Distributions (15%)

14. Bivariate distributions and

15. their properties,

16. distribution of sums and

17. quotients, conditional densities,

Module 4: Basic Statistics (15%)

18. Measures of Central tendency:

19. Moments, skewness and Kurtosis 

20. Probability distributions: Binomial, Poisson and Normal–

21. evaluation of statistical parameters for these three distributions,

22. Correlation and regression 

23. Rank correlation

Module 5: Applied Statistics(20%)

24. Curve fitting by the method of least squares- fitting of straight lines,

25. second-degree parabolas and

26. more general curves.

27. Test of significance:

28. Large sample test for single proportion,

29. difference of proportions,

30. single mean, difference of means, and

31. difference of standard deviations.

Module 6: Small samples (15%)

32. Test for single mean,

33. difference of means and

34. correlation coefficients,

35. test for ratio of variances –

36. Chi-square test for goodness of fit and

37.   independence of attributes.


1.    Axiomatic definitions of probability;

2.    conditional probability, independence &

3.    Bayes theorem,

4.    continuity property of probabilities, Borel-Cantelli Lemma;

Module-2

5.    random variable: probability distribution, density & mass functions, functions of a random variable

6.    expectation, characteristic & moment-generating functions;

7.    Chebyshev,

8.    Markov & Chernoff bounds;

Module-3

9.    jointly distributed random variables: joint distribution & density functions,

10. joint moments, conditional distributions & expectations,

11. functions of random variables;

Module-4

12. random vector- mean vector & covariance matrix,

13. Gaussian random vectors; sequence of random variables:

14. almost sure & mean-square convergences, convergences in probability & in distribution,

15. laws of large numbers, central limit theorem;

Module-5

16. random process: probabilistic structure of a random process;

17. mean, autocorrelation & auto covariance functions;

18. stationary - strict- sense stationary & wide-sense stationary (WSS) processes:

19. time averages & ergodicity;

20. spectral representation of a real WSS process

21. power spectral density, cross-power spectral density,

22. linear time-invariant systems with WSS process as an input- time & frequency domain analyses;

23. examples of random processes:

24. white noise,

25. Gaussian,

26. Poisson &

27. Markov processes


Module 01: Descriptive statistics

Presentation of Data: Frequency Distribution, Graphical Presentation of Data by Histogram, Frequency Curve & Cumulative Frequency Curves.

Measures of Central tendency & Dispersion: Mean, Median, Mode & their simple properties. Range, Mean Deviation, Quartile deviation, Standard Deviation, Coefficient of Variation.

Module 02: Probability theory

Probability: Random Experiment; Events; Algebra of Events; Counting techniques applied in probability problems; Conditional probability; General Multiplication Theorem; Independent events; Bayes’ theorem & related problems.

Module 03: Random variables & Distributions

Random variables (discrete & continuous); Probability mass function; Probability density function & distribution function. Expectation & Variance; Moment generating function; Probability Distributions—Binomial, Poisson, Normal, Exponential and Uniform; Chebychev inequality (statement) & problems.

Module 04: Correlation, Regression & Curve Fitting

Correlation & Regression: Bivariate Data, Simple Correlation & Regression, Pearson’s Correlation coefficient & its properties, Spearman’s Rank Correlation coefficient & its properties. Linear Regression & Regression equations, Regression coefficients & their properties. Multiple & Partial Correlation & Regression, Curvilinear Regression Curve Fitting: The Method of Least Squares-Linear & Non-Linear, Fitting of the curves of the form: y = a x + b, y = a x2 + b x + c and y = a ebx.

Module 05: Sampling techniques

Sampling: Concept of Population & Sample, Random Sample, Methods of drawing a simple random sample. Sample mean and variance, Sampling distribution, Test of Hypothesis, Level of significance, critical region, One tailed and two tailed tests, Interval Estimation of population parameters.

Module 06: Test of Significance & Analysis of Variance

Test of significance for Large samples: Test for significance of the difference between sample mean and population means, Test for significance of the difference between the means of two samples; Test of significance of small samples: Student’s t-distribution and its properties. Test for significance of the difference between sample mean and population mean, Test for significance of the difference between the means of two Samples, paired t-test. Chi-Square test for Independence of Attributes, Goodness of Fit & Homogeneity of Samples. Introduction to experimental Designs: Principles of Experimental Designs, Completely Randomized, Randomized Block & Latin Square Designs. Analysis of Variance (ANOVA) & Its use in the analysis of RBD.

BM-4502                                                                                                                   L-T-P-S-C

Operations Research                                                                                           4-0-0-0-4

 

Learning Outcomes: Learner will be able to

 

1.  To know optimizing techniques

 

2.  Understand special cases of LPP and apply in appropriate situation

 

3.  To appreciate the mathematical basis for business decision making

 

 

Course Content

Module 01: Linear Programming- Formulation, Solution by graph, Simplex, Duality,

 

post optimality and Sensitivity Analysis

 

Module02: Transportation problem with special cases Module03: Assignment Problem with special cases Module04: Game theory- Zerosum games

Module05: Decision Theory- Under Risk, Uncertainty, decision tree Module06: Waiting lines model- (M|M|1):(FIFO|∞|∞) with cost implication Module07: Simulation- queue system, inventory and demand simulation

 

 

Text/Reference Books



 

1.  Operations Research – AN introduction- HamdyTaha, Prentice Hall Of India

2.  Quantitative Techniques in Management -N D Vohra, Tata McGraw Hill

 

 

 

3.  Operations Research Theory and Applications- J K sharma, Macmillan Business

Books

4.  Principles of Operations Research –Wagner, Prentice Hall of India

5.  Operations Research- Hilier, Liberman, Tata McGraw HIll

6.  An introduction to Management Science – Anderson Sweeney Williams, Cengage

Learning

MA –1006                                                                        L–T–P–C                                      

Data analysis and interpretation                                   3–0–0– 3

Course Objectives: The objective of this course is to familiarize students with the basic statistical method used for engineering. Learn the fundamental techniques of data collection, interpretation, and analysis, and illustrate these techniques with application.

 

Course Outcomes:

After completion of this course students will be able to

·         CO1: Understand basic terminology of statistics and distributions and able to connect with real world problems.

·         CO:2 Understand the concept of classification and tabulation, chart and diagram, and statistical measures like measures of central tendency, dispersion.

 

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

1

1

 

 

 

 

 

 

 

 

 

1

 

Course Contents

 

Module 1: Collection of data: Classification and Tabulation

Meaning, characteristics and limitation of statistics, primary and secondary data, Population and sample, complete enumeration and sample survey, classification and tabulation.

Module 2: Chart and Diagrams

Advantage and disadvantage of charts and diagrams, types of charts and diagrams: line, bar, pie diagrams, histogram frequency polygon, and ogive.

Module 3: Frequency Distributions

Classification: Frequency Distribution Discrete & Continuous, Tabulation, simple series (grouped and ungrouped data) and frequency distribution, construction of frequency distribution, cumulative and relative frequency distribution, Diagrammatic representation, and frequency curve

Module 4: Measures of Central Tendency

Measures of Central Tendency: Arithmetic mean, median, mode, geometric mean, harmonic mean, partition values, Comparative analysis of all measures of Central Tendency

Module 5: Measures of dispersion

Measures of dispersion: range with coefficient of range, quartiles & quartile deviation with coefficient of quartile, mean deviation from mean with coefficient of mean deviation, standard deviation with coefficient of variance, skewness and kurtosis (only concept)

    

Text/Reference Books

  1. Fundamentals of Statistics. Gupta, S.C. Himalaya Publishing House
  2. Business Statistics, Gupta, S.P., & Agarwal A. Sultan Chand and Sons, New Delhi.
  3. Statistics (Schaum’s Outline Series). Spiegel M.R. Stephens L.J. Kumar N. McGraw Hill Education
  4. Statistical methods, Das N.G. The McGraw Hill Company Limited

5.    Fundamental of Mathematical Statistics, Gupta S. C., Kapoor V.K., Sultan Chand & Sons

 


Module 01: Introduction to Statistics

Introduction: Functions/Scope, Importance, Limitations

Data: Relevance of Data (Current Scenario), Type of data(Primary & Secondary), Primary(Census v/s Samples, Method of Collection (In Brief), Secondary(Merits, Limitations, Sources) (In Brief)


Presentation Of Data: Classification – Frequency Distribution – Discrete & Continuous, Tabulation, Graph (Frequency, Bar Diagram, Pie Chart, Histogram, Ogives)

Measures Of Central Tendency: Mean(A.M, Weighted, Combined), Median(Calculation and graphical using Ogives), Mode(Calculation and Graphical using Histogram), Comparative analysis of all measures of Central Tendency

Module02: Measures of Dispersion, Correlation and Linear Regression

Measures Of Dispersion: Range with C.R(Coefficient Of Range), Quartiles & Quartile deviation with CQ (Coefficient Of Quartile), Mean Deviation from mean with CMD (Coefficient of Mean Deviation), Standard deviation with CV(Coefficient of Variation), Skewness & Kurtosis (Only concept)

Correlation: Karl Pearson, Rank Correlation Linear Regression: Least Square Method Module03: Time Series and Index Number

Time Series: Least Square Method, Moving Average Method, Determination of Season Index Number: Simple(unweighted) Aggregate Method, Weighted Aggregate Method, Simple Average of Price Relatives, Weighted Average of Price Relatives, Chain Base Index Numbers, Base Shifting, Splicing and Deflating, Cost of Living Index Number

Module04: Probability and Decision Theory

Probability: Concept of Sample space, Concept of Event, Definition of Probability, Addition & Multiplication laws of Probability, Conditional Probability, Bayes’ Theorem(Concept only), Expectation & Variance, Concept of Probability Distribution(Only Concept)

Decision Theory: Acts, State of Nature Events, Pay offs, Opportunity loss, Decision Making under Certainty, Decision Making under Uncertainty,

Non-Probability: Maximax, Maximin, Minimax, Regret, Laplace &Hurwicz) Probabilistics (Decision Making under risk):EMV, EOL, EVPI Decision Tree

 

 

Text/Reference Books

1.    Statistics for Management. Richard L. Rubin D.S. Rastogi S. & Siddiqui H.M. 7thEd., Pearson Education.


2.    Business Statistics: A First Course. Levine D.M. Berenson M.L. Krehbiel T.C. Viswanathan P.K. Pearson Education.

3.    Practical Business Statistics. Siegel Andrew F. McGraw Hill Education.

4.    Business Statistics, Gupta, S.P., & Agarwal A. Sultan Chand and Sons, New Delhi.

5.    Business Statistics, Vohra N. D. McGraw Hill Education.

6.    Statistics (Schaum’s Outline Series). Spiegel M.R. Stephens L.J. Kumar N. McGraw Hill Education.

Fundamentals of Statistics. Gupta, S.C. Himalaya


BM-3502                                                                 L-T-P-S-C

Business Statistics                                                                                                4-0-0-0-4


Course Contents

Module 01:   Revision  of  Data  Representation,  Central  Tendency  and  Dispersion

 

Kurtosis and Skewness

 

Module02: Probability- Axioms, Addition and Multiplication rule, Types of probability,









Independence of events, probability tree, Bayes’ Theorem

 

Module03: Concept of Random variable, Probability distribution, Expected value and variance  of  random  variable,  conditional  expectation,  Classical  News  Paper  boys problem(EMV, EVPI)

Module04: Probability distributions Binomial, Poisson, Normal Module05: Sampling distribution

Module06: Estimation- Point estimation, Interval estimation Module07: Hypothesis testing- students t, Chi square, Z Module08: Analysis of variance- one-way and two way Module09: Correlation and regression, Analysis and significance

 

 

 

Text/Reference Books

1.  Statistics for Management. Richard L. Rubin D.S. Rastogi S. & Siddiqui H.M. 7th Ed.,

Pearson Education.

2.  Business  Statistics:  A  First  Course.  Levine  D.M.  Berenson  M.L.  Krehbiel  T.C.

Viswanathan P.K. Pearson Education.

3.  Practical Business Statistics. Siegel Andrew F. McGraw Hill Education.

4.  Business Statistics, Gupta, S.P., & Agarwal A. Sultan Chand and Sons, New Delhi.

5.  Business Statistics, Vohra N. D. McGraw Hill Education.

6.   Statistics (Schaum’s Outline Series). Spiegel M.R. Stephens L.J. Kumar N. McGraw

Hill Education.

7.   Fundamentals of Statistics. Gupta, S.C. Himalaya Publishing House

Probability Distribution:

 Curve Fitting:

Correlation , Linear regression.

Sampling Distributions:

Analysis of Variances:

 Queuing Models:


Course Content

Review of probability basics.

 Discrete & continuous distributions, common distributions (Poisson, exponential, Gaussian, etc.), functions of random variables, sums of random variables,

Multivariate Distributions, joint & marginal distributions,

 covariance & correlation,

sampling theory. Estimators, confidence intervals, hypothesis testing & P-values,

design of experiments.

 Markov Chains, Queuing Theory.


Sr. No.

Topics

Contact

Hours

(Lectures)

Part I:- Lesson Plan from start till first Mid Term Exams [12 lectures]

Introduction to Statistics(11 Lectures)

1.     

Introduction: Functions/Scope, Importance, Limitations

1

2.     

Data: Relevance of Data(Current Scenario), Type of data(Primary & Secondary), Primary(Census vs Samples, Method of Collection (In Brief), Secondary(Merits, Limitations, Sources) (In Brief)

3

3.     

 Presentation Of Data: Classification – Frequency Distribution – Discrete & Continuous, Tabulation, Graph(Frequency, Bar Diagram, Pie Chart, Histogram, Ogives)

3

4.     

Measures Of Central Tendency: Mean(A.M, Weighted, Combined), Median(Calculation and graphical using Ogives), Mode(Calculation and Graphical using Histogram), Comparative analysis of all measures of Central Tendency

4

Measures of Dispersion, Co-Relation and Linear Regression (13 Lectures)

5.     

Measures Of Dispersion:

Range with C.R(Co-Efficient Of Range),

1

Part II:- Lesson Plan after 1st Mid Term till 2nd Mid Term [12 lectures]

6.     

Quartiles & Quartile deviation with CQ (Co-Efficient Of Quartile),

2

7.     

Mean Deviation from mean with CMD (Co-Efficient Of Mean Deviation),

2

8.     

Standard deviation with CV(Co-Efficient Of Variance),

2

9.     

Skewness& Kurtosis (Only concept)

1

10.  

Co-Relation: Karl Pearson, Rank Co-Relation

2

11.  

Linear Regression: Least Square Method

3

Part III: - Lesson Plan after 2nd Mid Term till End Term. [14 lectures]

Time Series and Index Number: (08 Lectures)

12.  

Time Series: Least Square Method, Moving Average Method, Determination of Season,

3

13.  

Index Number: Simple(unweighted) Aggregate Method, Weighted Aggregate Method, Simple Average of Price Relatives, Weighted Average of Price Relatives, Chain Base Index Numbers, Base Shifting, Splicing and Deflating, Cost of Living Index Number

3

Probability and Decision Theory: (05 Lectures)

14.  

Probability: Concept of Sample space, Concept of Event, Definition of Probability, Addition & Multiplication laws of Probability, Conditional Probability, Bayes’ Theorem(Concept only), Expectation & Variance, Concept of Probability Distribution(Only Concept)

4

15.  

Decision Theory: Acts, State of Nature Events, Pay offs, Opportunity loss, Decision Making under Certainty, Decision Making under Uncertainty,

2

16.  

Non-Probability: Maximax, Maximin, Minimax, Regret, Laplace &Hurwicz), Probabilitistics (Decision Making under risk):EMV, EOL, EVPI, Decision Tree

2

Total Lectures

39