C) Statistics:(1) Probability: Random variables, Theorems of probability, Conditional probability, Independent events, Bayes theorem and its application, expectation, moments, distribution functions, Binomial, Poisson, Geometric, Exponential, Negative binomial, Hyper geometric, Cauchy, Laplace, Logistic, Pareto, Log-normal, Beta and Gamma distributions, Weibull, Uniform, Bivariate normal distribution and truncated distributions, Markov’s inequality, Chebyshev’s inequality, Cauchy-Schwarz inequality, Laws of large numbers, Central limit theorems and applications.
(2) Statistical Methods: Population and sample, Measures of central tendencies Parameter and Statistic, Correlation and Regression, intra-class correlation, multiple and partial correlations, Spearman s coefficient of rank correlation, Z, chi-square, t and F statistics and their properties and applications, Large sample distributions, Variance stabilizing transformations, sin inverse, square root, logarithmic and z transformation.
(3) Linear Models: General Linear models, BLUE, method of least squares, Gauss-Markoff theorem, estimation of error variance, Simple and Multiple linear regression models, Important assumptions and treatments in case of assumption’s violation, Regression diagnostics, Analysis of variance in one, two and three-way classifications, Analysis of Covariance in one and two-way classifications.
(4) Statistical Inference: Properties of estimators, MVUE, Rao-Blackwell and Lehmann-Scheffe theorems, Cramer-Rao inequality, methods of estimation, properties of maximum likelihood and other estimators, confidence intervals. Simple and composite hypotheses, Type I and Type II errors, size and power of a test, Most Powerful and Uniformly Most Powerful tests, Neyman-Pearson lemma, Likelihood Ratio test and its properties and applications. SPRT, OC and ASN functions, Tests of goodness of fit. Parametric vs. Non-parametric Test, Frequently-used non-parametric inferential statistical methods.
(5) Multivariate Analysis: Bivariate and Multivariate normal distribution, marginal and conditional distribution, Estimation of mean vector and covariance matrix, Asymptotic properties of estimators, Sampling distribution of and S, Mahalanobis D2 and Hotelling s T2 and its applications.
(6) Optimisation Techniques and Statistical Quality Control: Linear Programming, Transportation Problem, Assignment Problem, Basics of Simulation, Quality control, Process Control and Product Control, control charts, Acceptance Sampling plan, single and double sampling plans (ASN, OC, ATI, LTPD, AOQL).
(7) Sample Surveys and Design of Experiments: Simple and Stratified random sampling, ratio and regression methods of estimation, Double sampling, Systematic, Cluster, two stage and PPS sampling. Sampling and Non-sampling errors. Principles of Design of Experiments, Completely Randomized Design, Randomized Block Design, Latin Square Design, missing plot technique, 22 and 23 factorial designs, Split-Plot Design and Balanced Incomplete Block Design, Fractional factorial experiments
(8) Applied Economic Statistics: Time Series vs. cross sectional data, Multiplicative and additive models, Auto-correlation, Partial autocorrelation, Smoothing techniques, Seasonal and cyclical adjustment. Price and Quantity Index numbers, Types of index numbers and their properties. Chain and Fixed base index numbers, Cost of Living Index numbers, Wholesale Price Index, Consumer Price Index, Index of Industrial Production, Gini’s coefficient, Lorenz curves, Application of Pareto and Lognormal as income distributions.
(9) Vital Statistics: Sources of vital statistics compilation, Errors in census and registration data, Measurement of population, rate and ratio of vital events, Stationary and Stable population, Life Tables, Measures of Fertility, Mortality and Reproduction, Crude rates of natural growth, Pearl’s Vital Index.
(10) Numerical Analysis: Principles of floating point computations and rounding errors, Linear Equations factorization methods, pivoting and scaling, residual error correction method, Iterative methods, Jacobi, Gauss-Seidel methods, Newton and Newton like methods, unconstrained optimization, Lagrange interpolation techniques, Cubic Splines, Error estimates, Polynomials and least squares approximation; Integration by interpolation, adaptive quadratures and Gauss methods.
(11) Basic Computer Applications: Functional organization of computers, algorithms, basic programming concepts, Program testing and debugging, Subprograms and Subroutines, Sorting/searching methods, Database Management Systems, Software Engineering, Basic of Networking, Internet Technologies, Web and HTML, Distributed systems, Programming using C, MINITAB and FORTRAN.