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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. Post Graduate Semester Wise Syllabus 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. Bilinear forms, equivalence of Bilinear forms, quadratic forms, reduction of quadratic forms to canonical forms, orthogonal reduction of real quadratic form. Index and Signature of a quadratic form. 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. SUGGESTED READINGS: 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. Wads worth. 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) : Academic Publication Introduction to Matrix Analysis. 2nd Edn. Mc-Graw Hill. DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P. Post Graduate Semester Wise Syllabus 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) SUGGESTED READINGS : 1. Dudewicz E.J. and Mishra S.N. (1988) : Modern Mathematical Statistics. Wiley International (Student Edn. ) 2. Rohatgi V.K. (1984) : 3. Mukhopadhyay P. (1996) : An introduction to probability theory and mathematical statistics. Wiley Eastern Mathematical Statistics New Central Book Agency. DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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. Post Graduate Semester Wise Syllabus 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’ SUGGESTED READINGS: 1. : 2. Goon A.M.; Gupta M.K. and Das Gupta B. Mukhopadhyay, P 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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 III – Advanced Operation Research 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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. Post Graduate Semester Wise Syllabus 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. SUGGESTED READINGS: 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 Attributes Academic Press. Acceptance sampling in Quality Control Marcel – Dekkar SQC Methods, Marcel – Dekkar Sampling Inspection in SQC, Griffin, DEPARTMENT OF HIGHER EDUCATION, GOVT. OF M.P. Post Graduate Semester Wise Syllabus 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 : Advanced Operations Research : 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 models, Periodic Review Inventory System (PRIS), Advantages and disadvantages 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. SUGGESTED READINGS: 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. Hadely G. Addison Wesley. 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. Post Graduate Semester Wise Syllabus 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 SUGGESTED READINGS: 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. Madnani, G.M.K. (19--): Econometrics, Johnston, J. (1984): Econometric models, Third edition, McGraw Hill. 6. Klein,L.R. (1962): An Introduction to Econometrics, Prentice Hall of India 7. Koutsoyiannis, A. (1979) : Theory of Econometrics, Macmillan Press.

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