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```M.SC. Ist SEMESTER
Scheme of Examination:
There shall be four theory papers and two practicals in M.Sc. Ist Semester. Each theory
paper will be of 85 marks. Each practical examination will be of 50 marks. Continuous
Comprehensive Evaluation [CCE] is compulsory for each theory paper. The details of Scheme of
Examination and Distribution of Marks are as follows:
Paper/Paper-Title
Maximum Marks
Qualifying Marks
Theory
CCE
Total
Theory
CCE
Total
I – Linear Algebra
85
15
100
29
05
34
II – Distribution Theory - I
85
15
100
29
05
34
III – Sampling Techniques
85
15
100
29
05
34
IV – Measure Theory and probability
85
15
100
29
05
34
Practical – I Based on theory papers I & II
-
-
50
-
-
20
Practical – II Based on theory papers III & IV -
-
50
-
-
20
Semester Total
500
Qualifying
Mark
200
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
[email protected]
Max. Marks
Minimum Marks
Session 2014-2015
%
M.Sc. I Sem.
%
Semester I
%
Statistics
%
Linear Algebra
%
I
%
Compulsory
%
85
:
29
PARTICULARS
Unit – I
Unit- II
Unit– III
Unit-IV
Unit-V
Vector Space : Linear dependence, basis and dimension of a vector space, finite
dimensional vector space, vector subspace.
Inner Product Space and their properties, Schwartz Inequality, Triangle Inequality,
orthogonal basis and Gram-Schmidt Orthogonalization Process, Orthogonal projection
of a vector, linear simultaneous equations – Cramer’s rule.
Linear transformations and their properties, Partitioned matrices, Idempotent
Matrices, Kroneker Product, Hadamard Product, Hermite Canonical form,
Generalized inverse.
forms to canonical forms, orthogonal reduction of real quadratic form. Index and
Eigen values, Eigen Vectors and the characteristic equations of a matrix, Eigen Values
and Eigen vectors of a Linear Transformation. Cayley-Hamilton Theorem, Minimal
Polynomial. Multiplicity of Eigen values. Hermitian Matrices.
1.
Gray Bill, F.A. (1983)
:
2.
Scarle, S.R. (1982)
:
3.
Datta, K.B. (2006)
:
4.
Biswas, S (1984)
:
Matrices with applications in Statistics 2nd Ed.
Matrix Algebra Useful for Statistics. John Wiley
and Sons.
Matrix and Linear Algebra.
Prentice Hall of India EE. Edn.
Topics in Algebra of Matrices.
5.
Bellmen, R (1970)
:
Introduction to Matrix Analysis.
2nd Edn. Mc-Graw Hill.
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
[email protected]
Max. Marks
Minimum Marks
Session 2014-2015
%
M.Sc. I Sem.
%
Semester I
%
Statistics
%
Distribution Theory I
%
II
%
Compulsory
%
:
85
29
PARTICULARS
Unit – I
Random variable and it’s mathematical expectation, Conditional expectation, Joint,
Marginal and Conditional p.m.f.’s and p.d.f.’s.
Unit- II
Standard Discrete Distributions – The discrete Uniform Distribution, Binomial,
Truncated Binomial Hyper geometric, Poisson, Truncated Poisson, Geometric and
Negative Binomial Distributions.
Unit– III
Continuous Distributions – Continuous Uniform, Exponential, Gamma, Beta and
Cauchy Distribution.
Unit-IV
Normal, Lognormal, Laplace, Pareto, Weibull and Power series distribution.
Unit-V
Order statistics – Their distributions and properties, Joint and marginal distributions
of order statistics. Extreme values and their asymptotic distributions (statement only)
1.
Dudewicz E.J. and
Mishra S.N. (1988)
:
Modern Mathematical Statistics.
Wiley International (Student Edn. )
2.
Rohatgi V.K. (1984)
:
3.
:
An introduction to probability theory and
mathematical statistics. Wiley Eastern
Mathematical Statistics New Central Book Agency.
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
[email protected]
Max. Marks
Minimum Marks
Session 2014-2015
%
M.Sc. I Sem.
%
Semester I
%
Statistics
%
Sampling Techniques
%
III
%
Compulsory
%
85
:
29
PARTICULARS
Unit – I
Simple random sampling – definition, notations, properties of the estimates, variances of
the estimates f.p.c., Estimates of the standard error formula, sample confidence limits.
Stratified random sampling – Description, notations, properties of the estimates,
estimated variances and confidence limits. Proportional & Optimum allocation, relative
precision of stratified random and simple random sampling.
Unit- II
Stratified random sampling - Estimation of sample size with continuous data, stratified
sampling for proportions, gains in precision in stratified sampling for proportions,
estimation of sample size with proportions.
Ratio Estimators – Methods of Estimations, Ratio estimate, Approximate variance of the
Ratio Estimate, Estimation of the Variance from a sample, confidence limits, comparison
of the Ratio Estimate with mean per unit, conditions under which the ratio estimate is
BLUE, Bias of the Ratio Estimate.
Unit– III
Regression Estimate – The linear regression Estimate, Regression estimate with pre
assigned b, Regression estimate when b is computed from the sample, sample estimate of
variance, large sample comparison with the Ratio estimate and the mean per unit. Bias
of the Linear Regression estimate.
Systematic Sampling – Description, notations, relation to cluster sampling, variance of
the estimated mean, Populations with Linear trend, Comparison of systematic with
Stratified and Simple Random sampling.
Unit-IV
Single stage cluster sampling (Clusters of equal Size) – definition, notations, Reasons for
Cluster Sampling, Comparisons of precision made from survey data, variance in terms
of Intracluster Correlation, Cluster sampling for proportions.
Cluster of Unequal Size– Cluster units of unequal size, Selection with Unequal
probabilities with replacement, Relative accuracies of Three Techniques, Sampling with
unequal probabilities without replacement, The Horvitz – Thomson Estimator.
Unit-V
Subsampling with units of Equal Size/two stage sampling, Finding means and variances
in two-stage sampling, variance of the estimated mean in two-stage sampling, sample
estimation of the variance.
Subsampling with units of unequal size – introduction, sampling methods when n=1 and
n>1, two useful Results, Units selected with equal probabilities : Unbiased Estimator and
Ratio to size estimate.
Double Sampling – Description of the Technique, Double sampling for stratification,
optimum allocation, Estimated variance in Double sampling for stratification.
1.
Cochram, W.G.
:
2.
Singh D and Choudhary F.S.:
3.
Sukhatme
:
4.
Murthy M.N.
:
Sampling Techniques.
Wiley Eastern
Theory and Analysis of Sample surveys designs.
Wiley Eastern.
Sampling Theory of surveys
With application. IARS, New Delhi
Sampling Theory and Methods.
Statistical Publishing Society Calcutta.
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Minimum Marks
Session 2014-2015
%
M.Sc. I Sem.
%
Semester I
%
Statistics
%
Measure Theory and Probability
%
IV
%
Compulsory
%
85
:
29
PARTICULARS
Unit – I
Classes of Sets, Fields, Sigma Fields, Minimal Sigma-Field, Lim Superior and Lim
inferior of Sets. Measure, Probability of Measure. Properties of measure.
Lebesgue and Lebesgue – Steljes Measures Measureable Functions, Random Variable,
Unit- II
Sequence of Random Variables, Almost Sure Convergence, Convergence in Probability
and in Measure.
Unit-III
Integration of a Measurable functions with respect to a measure, Monotone convergence.
Unit-IV
Borell – Cantelli Lemma, Independence, Weak and Strong Law of Large Numbers for
I.I.D. Sequences, Definition and examples of Markov dependence.
Unit-V
Convergence in distribution, characteristic function, Uniqueness theorem, Statement of
Levy’s Continuity Theorem, Central Limit Theorem for a Sequence of independent
variables under Lindeberg’s Conditions, Central limit Theorem for I.I.D. random
variables.
1.
Billingsley. P (1986)
:
2.
Kingman, JFC and
:
Probability and Measure .
Wiley International
Introduction to Measure and
Taylor, S.J. (1966)
3.
Gupta K.P.
:
Probability, Cambridge Univ.
Press
Measure Theory
M.SC. IInd SEMESTER
Scheme of Examination:
There shall be four theory papers and two practicals in M.Sc. IInd Semester. Each theory
paper will be of 85 marks. Each practical examination will be of 50 marks. Continuous
Comprehensive Evaluation [CCE] is compulsory for each theory paper. The details of Scheme of
Examination and Distribution of Marks are as follows:
Paper/Paper-Title
Maximum Marks
Qualifying Marks
Theory
CCE
Total
Theory
CCE
Total
I – Real Analysis
85
15
100
29
05
34
II – Distribution Theory – II
85
15
100
29
05
34
III – Statistical Computing
85
15
100
29
05
34
IV – Statistical Inference
85
15
100
29
05
34
Practical – I Based on theory paper I & II
-
-
50
-
-
20
Practical – II Based on theory paper III & IV
-
-
50
-
-
20
Qualifying
Mark
200
Semester Total
500
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Minimum Marks
Session 2014-2015
%
M.Sc. II Sem.
%
Semester II
%
Statistics
%
Real Analysis
%
I
%
Compulsory
%
85
:
29
PARTICULARS
Elements of Set Theory – Introduction to real numbers, n-dimensional Euclidian space, Open
Unit-I
and Closed intervals, Compact Sets, Bolzano–Weirstrass and Heine–Borel theorems.
Sequences and Series; Their convergence, Real valued functions, Continuous functions,
Unit-II
Uniform Continuity.
Unit-III
Sequences of functions, Uniform Convergence, Power Series and radius of convergence.
Unit-IV
Differentiation : Maxima–Minima of functions, Functions of several variables, Constraints,
Maxima-Minima of functions.
Unit-V
Multiple integrals and their evaluation by repeated integration, change of variable in multiple
integration, uniform convergence in improper integrals, differentiation under the sigh of
integration-Leibritz Rule.
1.
Apostol, T.M.
:
2.
Rudin Walter (1976)
:
3.
Mullik, S.C.
:
Mathematical Analysis Narosa.
Indian Edn.
Principles of Mathematical Analysis
Mc-Graw Hill
Mathematical Analysis. Wiley Easern Ltd.
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Minimum Marks
Session 2014-2015
%
M.Sc. II Sem.
%
Semester-II
%
Statistics
%
Distribution Theory II
%
II
%
Compulsory
%
85
:
29
PARTICULARS
Jointly distributed random variable Distribution function of Joint distribution, Marginal
Unit-I
distribution, Conditional distributions and Independence of X and Y. Discrete and Continuous
Two-dimensional distribution, Moments of conditional distributions.
Simple correlation and regression, Non-linear regression, regression of the second kind,
Unit-II
correlation index and correlation Ratio, Bivariate Normal distribution.
Unit-III
Sampling distribution of a function of random variables. case of discrete and continuous
variables. Three basic sampling distributions chi-square, t and F-distributions.
Sampling distributions arising from a univariate Normal distribution (Sample mean, Sample
Variance).
Unit-IV
Non central chisquare, t and F distributions, their properties and applications.
Unit-V
Distributions arising from the bivariate normal (Linear functions of two jointly distributed
normal variables). Sampling distribution of sample means, variance and covariances in
bivariate normal situation Sampling distribution of ‘r’
1.
:
2.
Goon A.M.; Gupta M.K. and
Das Gupta B.
3.
Gupta S.C., Kapur V.K.
:
:
An outline of statistical Theory
Vol. I World Press Calcutta.
Mathematical Statistics.
Central Book Agency.
Fundamentals of Mathematical Statistics.
4.
Agrawal, B.L.
:
Sultan Chand and Sons
Basic Statistics New Age
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Minimum Marks
Session 2014-2015
%
M.Sc. II Sem.
%
Semester-II
%
Statistics
%
Statistical Computing
%
III
%
Compulsory
%
85
:
29
PARTICULARS
Statistics for National development; Estimation of National Income-Product approach, Income
Unit-I
approach and Expenditure approach. Measuring inequality in income, Ginnie’s Coefficient.
History of Computers, Basic Building blocks-Input / Output devices, CPU organization,
Unit-II
Storage devices – Primary and Secondary memory, Fundamentals of operating systems (O.S.)
Def. and need of O.S., Functions and Types of O.S.; M.S.-DOS Fundamentals, Booting
Process (Cold & Warm) file arrangement in DOS. Internal and External DOS Commonds.
Unit-III
Problem Solving on Computers : Algorithm and FLOW charts. FORTRAN Programming
preliminaries - Constants and Variables. Arithmetic, relational and logical operations and
expressions. Executable and Non – executable FORTRAN Statements. Input / Output
Statements, Arrays and Subscripted Variables.
Unit-IV
Simple Computer programmes in FORTRAN related to statistics such as – Mean, Median,
Mode, Histogram. Variance, Simple Correlation Coefficient, Regression Lines and regression
coefficient. Curve fitting using least square theory.
Unit-V
Statistical Package SPSS-Its use in graphics descriptive statistics, representation of
multivariate data. Simple Hypothesis Tests, Analysis of Variance and Linear regression.
1.
2.
3.
C.S.O. (1980)
Rajaraman V.
Taxali, R.K.
:
:
:
National Statistics – Source and Health.
Computer Programming in FORTRAN.
P.C. Software made Simple. Mc-Graw Hill
4.
Sabine L. and Brian, S.E. (2003):
A Handbook of Statistical Analysis using SPSS.
Taylor and Francis Books
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Minimum Marks
Session 2014-2015
%
M.Sc. II Sem.
%
Semester-II
%
Statistics
%
Statistical Inference
%
IV
%
Compulsory
%
85
:
29
PARTICULARS
Unit-I
Unit-II
Unit-III
Unit-IV
Unit-5
Point estimation : Methods of estimation - Maximum likelihood method, method of moments
and percentiles, choice of estimators based on unbiasedness, minimum variance, mean squared
error, minimum variance unbiased estimators.
Rao-Blackwell Theorem, Completeness, Lehmann–Scheffe Theorem, Necessary and
sufficient conditions for MVUE Cramer-Rao Lower bound.
Tests of Hypothesis, Concepts of critical regions, Two Kinds of errors, size function, power
function, level, MP and UMP test in class of small size tests.
Wald’s SPRT with prescribed error of Two Types, Neymann-Pearson Lemma, MP test for
Simple Null against Simple alternative hypothesis, UMP tests for simple Null hypothesis
against one side alternative and against Null against one sided alternative in one parameter
exponential family.
Standard one sample and two sample non-parametric tests for location.
Interval estimation, Confidence level, Construction of Confidence intervals using Pivots,
Shortest expected length confidence interval.
1.
Kale, B.K. (1999)
:
2.
3.
4.
Lehman, E.L. (1986)
Lehman,. E.L. (1986)
Rao, C.R. (1973)
:
:
:
A first Course in parametric inference, Narosa
Publishing House.
(Latest) Theory of Point Estimation Student Edn.
Testing Statistical Hypothesis
Linear Statistical inference & it’s applications.
M.SC. IIIrd SEMESTER
Scheme of Examination:
There shall be four theory papers and two practicals in M.Sc. IIIrd Semester. Each theory
paper will be of 85 marks. Each practical examination will be of 50 marks. Continuous
Comprehensive Evaluation [CCE] is compulsory for each theory paper. The details of Scheme of
Examination and Distribution of Marks are as follows:
Paper/Paper-Title
Maximum Marks
Qualifying Marks
Theory
CCE
Total
Theory
CCE
Total
I – Multivariate Analysis
85
15
100
29
05
34
II – Linear Models
85
15
100
29
05
34
III – Operation Research
85
15
100
29
05
34
IV – Programming with Language ‘C’
85
15
100
29
05
34
Practical – I Based on theory paper I & II
-
-
50
-
-
20
Practical – II Based on theory paper III & IV
-
-
50
-
-
20
Qualifying
Marks
200
Semester Total
500
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Min. Marks
Session 2014-2015
:
M.Sc. III Sem.
:
Semester III
:
Statistics
:
Multivariate Analysis
:
I
:
Compulsory
:
85
:
29
PARTICULARS
Unit-I
Unit-II
Unit-III
Unit-IV
Unit-V
Multivariate normal distribution and its properties. Random sampling from a
Multivariate normal distribution. Maximum likelihood estimate of parameters.
Distribution of sample mean vector. Wishart matrix-its distribution and properties.
Distribution of sample generalized variance.
Null and Non-null distribution of sample correlation coefficient. Null distribution of
partial and multiple correlation coefficient. Distribution of sample regression
coefficient.
Null distribution of Hotlling’s T2 statistic. Application in tests on mean vector for
one and more multivariate normal population and also on equality of the components
of mean vectors in multivariate normal population.
Classification and discrimination procedures for discrimination between two
multivariate normal populations. Principal components and cannonical variates.
 Andrson, T.W. (1983)
:
Wiley
 Kishirsaghar, A M (1972) :
 Giri, N.C. (1977)
:
 Sharma, S (1996)
:
 Shrivastava, M.S. and
:
Khatri, C.G. (1979)
An introduction to multivariate statistical analysis - II edd.
Multivariate analysis - Marcel Dekkar.
Multivariate Statistical Inference - Academic Press.
Applied Multivariate Techniques – Wiely.
An Introduction to Multiveraite Statistics.
North Holand
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Min. Marks
Session 2014-2015
:
M.Sc. III Sem.
:
Semester III
:
Statistics
:
Linear Models
:
II
:
Compulsory
:
85
:
29
PARTICULARS
Unit-1
Unit -2
Unit-3
Unit-4
Unit-5
Gauss – Makov Setup – Estimability, best point estimates and interval estimates of estimable
linear parametric function. Normal equation and least square estimates.
Error and estimation spaces, variances and covariance’s of least square estimates. Estimation
of error variance, estimations with correlated observations. Least squares estimates with
restriction on parameters, simultaneous estimates of Linear parametric functions.
Tests of hypothesis for one and more than one linear parametric function. Confidence interval
and regions power of F-test, Multiple comparison test due to Tukey and Scheffe,
Simultaneous confidence intervals.
Introduction to one-way random effect Linear models. Estimation of variance components.
Multiple regression. Fit of orthogonal polynomials and its uses.
Introduction to non-Linear models. Estimations of parameters in case of Multi-collinearity
and Ridge regression. Principal component regression.
1.
Cook, R.D. and Weisberg, S. (1982) :
2.
Draper N.R. & Smith H (1998)
3.
Gunst, R.F. and Mason R.L. (1980) :
4.
Weisberg S. (1985)
:
5.
Reo C.R. ( 1973)
application
:
:
Residual and influence in regression
Champman & Hall
Applied regression analysis
3rd Edition - Wiley
Regression analysis and Application
Marcel Dekker
Applied Linear Regression
Wiley
Linear Statistical inference and
its
Wiley Estern.
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory/Optional
Max. Marks
Min. Marks
Session 2014-2015
:
M.Sc. III Sem.
:
Semester III
:
Statistics
:
Operations Research
:
III
:
Optional
:
85
:
29
PARTICULARS
Unit-I
Unit-II
Unit-III
Unit-IV
Unit-V
Definition and Scope of O.R., Phases of O.R., Linear Programming Problems:
Graphical, Simplex, Artificial Variable Techniques, Big M, Two phase methods.
Degeneracy and methods for resolving it.
Revised Simplex Algorithm in standard form-I. Duality in Linear Programming
Problems. Duality theorems - Basic Duality Theorem, Fundamental Duality Theorem
and Existence Theorem. Advantages of duality.
Transportation and Assignment problems with proofs of relevant result and methods
of solutions, Goal Programming – Concepts, Goal Programming as an extension of
LP, Single Goal Models.
Integer Linear Programming – Definition, importance and need of integer
programming. Gomory’s cutting plane method. Geometric interpretation of
Gomory’s cutting plane method. Branch and bound method. Geometrical
interpretation of Branch & bound method. Applications of Integer Programming.
Non-Linear Programming Problems – Definition, practical situation, formulation of
Non-Linear Programming Problems, General Non-Linear Programming Problems.
Canonical form of Non-Linear Programming Problem. Graphical solution and
verification of Kuhn–Tucker conditions. Quadratic Programming–Definition, Kuhn–
Tucker conditions. General Quadratic Problem – Wolfe’s and Beals’s Methods.
 Sharma, S.D. (2005)
 Kanti Swaroop, Gupta P.K.
:
:
Operations Research - Kedar Naik Ram Naik & Co.
Operations Research - Sultan Chand & Sons.
and Man Mohan Singh
 Taha H A
 Wagner H M
:
:
Operations Research – Mac Millon
Principles of Operations Research with application
Prentics – Hall.
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Session 2014-2015
:
M.Sc. III Sem.
:
Semester III
:
Statistics
:
Programming with Language C
:
IV
:
Optional
:
85
:
29
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Min. Marks
PARTICULARS
Unit-I
Introduction to C; C-Fundamentals : Character set identifiers of Key words.
Constants, variables, arrays, declarations, expressions and statements.
Unit-II
Operators and Expressions – Arithmetic operators Relational and logical operators
Assignment Operators. Conditional operators and Library function.
Unit-III
Data Input and output – Preliminaries, Singal Character input single character output,
Entering input data, Writing output data. Control Statements : While, Do-While, for,
if-else, Switch, Break, Continue and go to Statement.
Unit-IV
Function, Arrays and Pointers.
Unit-V
Writing Simple Programme related to statistics in ‘C’ – Such as Mean, Median,
Variance. Correlation, regression, root extraction matrix computation, Numerical
integration random number generation, ANOVA etc.
 Byron S Gottfried
:
Programming with C – Tata Mc-Graw-Hill
 Balaguru Swamy, E :
Programming in ANSIC - Tata Mc-Graw-Hill
BW Krmghan and
:
The C-Programming Language – Prentice Hall
:
Let Us ‘C’
D.M. Ditchie (1988)
 Kantekar, Y
M.SC. IVth SEMESTER
Scheme of Examination:
There shall be four theory papers and two practicals in M.Sc. IVth Semester. Each theory
paper will be of 85 marks. Each practical examination will be of 50 marks. Continuous
Comprehensive Evaluation [CCE] is compulsory for each theory paper. The details of Scheme of
Examination and Distribution of Marks are as follows:
Paper/Paper-Title
Maximum Marks
Qualifying Marks
Theory
CCE
Total
Theory
CCE
Total
I – Design of Experiments
85
15
100
29
05
34
II – Statistical Quality Control
85
15
100
29
05
34
85
15
100
29
05
34
IV – Econometrics
85
15
100
29
05
34
Practical – I Based on theory paper I & II
-
-
50
-
-
20
Practical – II Based on theory paper III & IV
-
-
50
-
-
20
Qualifying
Marks
200
Semester Total
500
Internship / Job Oriented Project
Duration
Marks
-
60 hours
100
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Min. Marks
Session 2014-2015
:
M.Sc. IV Sem.
:
Semester IV
:
Statistics
:
Design of Experiments
:
Paper I
:
Compulsory
:
85
:
29
PARTICULARS
Unit-I
Unit-II
Unit-III
Unit-IV
Unit-V
Introduction to design of experiments – Completely randomized design (CRD),
Randomized block design (RBD), Latin Square design (LSD), Graeco Latin square
design, Cross-over designs. Missing plot technique–general theory and applications.
Analysis of co-variance : ANOCOVA for one way classification with single
concomitant variable in CRD layout, ANOCOVA for two way classification with
single concomitant variable in RBD layout, application to standard designs. Split
Plot and Split Block experiments.
General Block Design, Information matrics ‘C’ and its properties, Concept of
connectedness, orthoganality, balance and partial balance, Analysis of block designs.
Balanced incomplete block design (BIBD) – Definition, Parameters of BIBD,
Parametric relations for existence of BIBD, Symmetric BIBD, Analysis with intra
block information and recovery of inter block information PBIBD, Youden design.
General Factorial experiments, factorial effects, best estimates and testing the
significance of factors-effects; study of 2n (n≤4) and 3n (n≤3) factorial expermints
in randomized blocks, complete and partial counfouding.
 Das M. N. and Giri, N.C. (1979) : Design & Analysis of Experiment – Wiley Estern





Aloke Day (1986) : Theory of Block Design - Wiley Estern
Angela Deal and Daniel Voss (1999) : Design and Analysis of Experiments Springer
Giri N. (1986) : Analysis of Variance – Asia Publisher
John PW (1971) : Statistical Design and Analysis of Experiments – Mac Millon
Montegomery C D (1976) : Design and Analysis of Experiments – Wiley.
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory/Optional
Max. Marks
Min. Marks
Session 2014-2015
:
M.Sc. IV Sem.
:
Semester IV
:
Statistics
:
Statistical Quality Control
:
II
:
Compulsory
:
85
:
29
PARTICULARS
Unit-I
Unit-II
Unit-III
Unit-IV
Unit-V
Meaning and scope of SQC, Shewhart control charts for 𝑋̅, R, np, p, c etc and their
uses. OC and ARL of control charts, uses of runs and related pattern of points.
Control charts based on C.V., extreme values, moving averages, Geometric moving
averages, modified control charts.
Cusum charts, use of V-mask, derivation of ARL. Joint use of Shewhart and Cusum
charts. Economic design of control charts.
Sampling inspection plans – Classification and general properties. Sampling plans
by variables, estimation of lot defective and plan parameter determination in known
and unknown cases.
Continuous Sampling Plans: CSP-A and CSP-B of Wald and Wolfowitz and their
properties. Curtailed and Semi Curtailed Sampling Plans.
Basics of Six-Sigma – Origin and meaning of Six-Sigma, importance and
applicability of Six-Sigma, environment for Six-Sigma and implementation of SixSigma.
 Juran J.M. & Gryna F.M. (1980)
:
Quality planning and analysis
Tata Mc Gram Hill
 Montgomery, D.C.
:
 Wald, A (1981)
:
 Schilling E.G. (1981)
:
 Burr I.W. (1976)
 Guenthor N.C. (1977)
Landon.
:
:
Introduction to Statistical
Quality control, John Wiley
Statistical Theory of Sampling by
Acceptance sampling in Quality Control
Marcel – Dekkar
SQC Methods, Marcel – Dekkar
Sampling Inspection in SQC, Griffin,
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Min. Marks
Session 2014-2015
:
M.Sc. IV Sem.
:
Semester IV
:
Statistics
:
:
Paper III
:
Optional
:
85
:
29
PARTICULARS
Unit-I
Theory of games – Basic definitions, Minimax (Maximin) criterion, saddle point,
optiomal strategies and value of the game, games with and without saddle points,
equivalence of rectangular game of L.P. Fundamental of game theory, solution of
m×n game by LP 2×2 games without saddle point, principle of dominance,
graphical method for 2xn and mx2 games, business application (Bidding problems).
Unit-II
Inventory management – Preliminaries, EOQ, deterministic elementary static
demand. Inventory models (Model - I,II, III). Fluctuating (Dynamic) demand
of PRIS.
Probabilistic inventory models : Instantaneous Demand, No Setup Cost (Discrete
and Continuous case).
Unit-III
Replacement – Replacement problem of items that deteriorate and replacement of
items that fail completely. Individual replacement policy, mortality theorem, group
replacement policy, recruitment and promotion problems. Equipment renewal
problem.
Unit-IV
Waiting line models : Queueing system. Transient and steady states. Traffic
intensity, Probability distribution in queuing systems. Solution of (M/M/1) :
(∞/FCFS) – Erlang model, (M/M/1); (N/FCFS); (M/M/S) : (∞/FCFS); (M/Ek/1) :
(FCFS); (M/G/1) : (∞/GD) Queuing models.
Unit-V
Job Sequencing : Terminology and notations. Processing n jobs through 2 machines,
n Jobs through 3 machines, 2 Jobs through m machines, n Jobs through m machines.
Project management PERT and CPM : Basic steps in PERT/PCM techniques rules
for drawing network diagram, time estimates and critical path in network analysis;
Evaluating optimistic most likely, Pessimistic and expected time in PERT.
Application areas of PERT/CPM.
1.
Sharma S.D.
:
Operations Research – Kendarnath Ramnath & Co.
2.
Kantiswaroop Gupta P.K.
:
Operations Research. Sultan Chand & Son
:
Non Linear and Dynamic Programming,
& Singh M.
3.
4.
Keinrock, L.
:
Queuing System Vol - I, John Wiley
5.
Mckinsey, J.C.C
:
Introduction to game theory, McGraw Hill
6.
Grass D, Harris C.M.
:
Fundamentals of Queueing theory – John Wiley
DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P.
As recommended by Central Board of studies and Approved by the
Governor of M.P.
f’k{kk foHkkx- e-iz- 'kklu
LukrdksRrj d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;Øe
dsanzh; v/;;u e.My }kjk vuq’kaflr rFkk e-iz- ds jkT;iky }kjk
vuqeksfnr
Class
Semester
Subject
Title of Subject Group
Paper No.
Compulsory Optional
Max. Marks
Min. Marks
Session 2014-2015
:
M.Sc. IV Sem.
:
Semester IV
:
Statistics
:
Econometrics
:
Paper IV
:
Optional
:
85
:
29
PARTICULARS
Unit-I
Unit-II
Unit-III
Unit-IV
Unit-V
Nature of Econometrics – The general linear model (GLM) and its extensions ordinary
least squares (OLS) estimation and prediction. Use of dummy variables and seasonal
adjustment. Generalized least squares (GLS) estimation and prediction. Heteroscedastic
disturbances.
Auto Correlation, its consequences and tests. Theil BLUS procedure. Multicollinearity
problem, Its implication and tools for handing the problem.
Linear regression with stochastic regressors. Instrumental variable estimation. Errors in
variables. Auto regressive linear regression. Distributed lag models.
Use of Principal components, Canonical correlations and Discriminant analysis in
econometrics.
Simultaneous linear equation model – Examples, Identification problem, Restriction on
structural parameters – rank and order conditions. Restrictions on variances &
covariances.
Estimation in simultaneous equation model. Recursive systems. 2SLS estimators,
Limited information estimators, 3SLS estimation, Full information maximum likelihood
method predication
1.
2.
3.
4.
5.
Apte PG (1990) : Text book of Econometrics. Tata McGraw Hill.
Cramer, J.S. (1971) : Empirical Econometrics, North Holland.
Gujarathi, D (1979) : Basic Econometrics, McGraw Hill.