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
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Available courses
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 TabulationModule 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
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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. |
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4
4
4
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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,
MumbaiCourse 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.
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1. Axiomatic definitions of probability; |
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2. conditional probability, independence & |
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3. Bayes theorem, |
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4. continuity property of probabilities, Borel-Cantelli Lemma; |
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Module-2 |
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5. random variable: probability distribution, density & mass functions, functions of a random variable |
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6. expectation, characteristic & moment-generating functions; |
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7. Chebyshev, |
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8. Markov & Chernoff bounds; |
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Module-3 |
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9. jointly distributed random variables: joint distribution & density functions, |
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10. joint moments, conditional distributions & expectations, |
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11. functions of random variables; |
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Module-4 |
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12. random vector- mean vector & covariance matrix, |
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13. Gaussian random vectors; sequence of random variables: |
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14. almost sure & mean-square convergences, convergences in probability & in distribution, |
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15. laws of large numbers, central limit theorem; |
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Module-5 |
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16. random process: probabilistic structure of a random process; |
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17. mean, autocorrelation & auto covariance functions; |
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18. stationary - strict- sense stationary & wide-sense stationary (WSS) processes: |
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19. time averages & ergodicity; |
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20. spectral representation of a real WSS process |
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21. power spectral density, cross-power spectral density, |
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22. linear time-invariant systems with WSS process as an input- time & frequency domain analyses; |
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23. examples of random processes: |
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24. white noise, |
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25. Gaussian, |
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26. Poisson & |
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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
LearningMA –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.
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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
- Fundamentals of Statistics. Gupta, S.C. Himalaya Publishing House
- Business Statistics, Gupta, S.P., & Agarwal A. Sultan Chand and Sons, New Delhi.
- Statistics (Schaum’s Outline Series). Spiegel M.R. Stephens L.J. Kumar N. McGraw Hill Education
- 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 HouseProbability Distribution:
Curve Fitting:
Correlation , Linear regression.
Analysis of Variances:
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.
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Sr. No. |
Topics |
Contact Hours (Lectures) |
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Part I:- Lesson Plan from start till first Mid Term Exams [12 lectures] |
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Introduction to Statistics(11 Lectures) |
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1. |
Introduction: Functions/Scope, Importance, Limitations |
1 |
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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 |
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3. |
Presentation Of Data: Classification – Frequency Distribution – Discrete & Continuous, Tabulation, Graph(Frequency, Bar Diagram, Pie Chart, Histogram, Ogives) |
3 |
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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 |
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Measures of Dispersion, Co-Relation and Linear Regression (13 Lectures) |
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5. |
Measures Of Dispersion: Range with C.R(Co-Efficient Of Range), |
1 |
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Part II:- Lesson Plan after 1st Mid Term till 2nd Mid Term [12 lectures] |
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6. |
Quartiles & Quartile deviation with CQ (Co-Efficient Of Quartile), |
2 |
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7. |
Mean Deviation from mean with CMD (Co-Efficient Of Mean Deviation), |
2 |
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8. |
Standard deviation with CV(Co-Efficient Of Variance), |
2 |
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9. |
Skewness& Kurtosis (Only concept) |
1 |
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10. |
Co-Relation: Karl Pearson, Rank Co-Relation |
2 |
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11. |
Linear Regression: Least Square Method |
3 |
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Part III: - Lesson Plan after 2nd Mid Term till End Term. [14 lectures] |
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Time Series and Index Number: (08 Lectures) |
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12. |
Time Series: Least Square Method, Moving Average Method, Determination of Season, |
3 |
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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 |
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Probability and Decision Theory: (05 Lectures) |
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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 |
|