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CSIR Syllabus

Mathematics Paper I Continued

14. Statistical methods and Data Analysis  :  Tests for mean and variance in the normal distribution :  one – population and two – population cases ; related confidence intervals.  Tests for product moment, partial and multiple correlation coellicients ; comparison of k linear regressions.   Fitting polynomial regression ;  related test.  Analysis of discrete data ;  chi-square test of goodness of fit, contingency tables.  Analysis of variance one – way and two – way classification ( equal number of observations per cell ).  Large sample tests through normal approximation.  Nonparametric tests ; sign test , median test, Mann – Whitney test, Wilcoxen test for one and two – samples, rank correlation and test of independence.

15. Operational Research Modeling  :  Definition and scope of Operational Research.  Different types of models.  Replacement models and sequencing theory, inventory problems and their analytical structure.  Simple deterministic and siochastic models of inventory control.  Basic characteristics of queueingsystem, different performance measures.  Steady state solution of Markovian queueingmodels :  M/M/1, WW1 with limited waiting space MWC, M/M/C with limited waiting space.

16. Linear Programming  :  Linear Programming, Simplex method, Duality in linear programming.  Transformation and assignment problems.  Two person – zero sum games.  Equivalence of rectangular game and linear programming.

17. Finite Population  :  Sampling Techniques and Estimation :  Simple random sampling with and without replacement.  Stratified sampling ; allocation problem ; systematic sampling.  Two stage sampling, Related estimation problems in the above cases.

18. Design of Experiments  :  Basic principles of experimental design.  Randomisation structure and analysis of completely randomized, randomized blocks and Latin – square designs.  Factional experiments.  Analysis of 2n factional experiments in randomized blocks.