Civil Service Statistics Main Exam Paper One Syllabus
PAPER-1
1 PROBABILITY
Sample space and events, probability mesure and probability space, random variable as a measurable function,distribution function of random variable, discrete and continuous type random variable, probability mass function, probability density function, vector-valued random variable, marginal and conditional distributions, stochastic independence of events and of random variables, exectation ad moments of random variable,conditional expectation , convergence of sequence of random variable in distribution, in probability ,in pth mean and lamost everywhere, their criteria and inter-relations Chebyshew’s inequality and Khintchine’s weak laws of large numbers, strong law of large numbers and Kolmogoroff’s theorems,probability generating function,moment generating function, characteristic function, inversion theorem, Linderberg and Levy forms of central limit theorem , standard discrete and continuous proability distributions.
II Statistical Inference
Consistency, unbiasedness, efficiency,cufficiency, completeness, ancillary statistics, factorization theorem, exponential family of distribution and its properties, uniformly minimum variance unbiased (UMVU) estimation,Rao-Backwell and Lehmann-Schefee theorems, Cramer-Rao inequality for single parameter:Estimation by methods of moments, maximum likelihood,least squares,minimum chi-square and modified minimum chi-square,properties of maximum likelihood and other estimator asymptotic efficiency,prior and posterior distribution ,loss function risk function risk function and minimax estimator Bayyes estimators
Non-randomised and randomized tests, critical function,MP tests,Neyman-Pearson lemma,UMP tests, monotone likelihood ratio,similar and unbiased tests,UMPU tests for single parameter likelihood ratio test its asymptotic distribution.Confidence bounds and its relation with tests.
Kolmogoroff’s test for goodness of fit and its consistency,sign test and its optimality.Wilcoxon signed-ranks test and its consistency,Kolmogorov two-sample test ,run test, Wilcoxon-Mann-Whitney test and median test, their consistency and asymptotic normality.
Wald’s SPRT and its properties,OC and ASN functions for tests regarding parameters for Bernoulli poisson, normal and exponential distribution .Wald’s fundamental identity
III.Linear Inference and Multivariate Analysis
Linear statistical models, theory of least squares and analysis of variance,Gauss-Markoff theory normal equations,least squares estimates and theior precision,test of significance and interval estimates based on least squares theory in one-way,two-way and three-way c;assified data,regression analysis linear regression , curvilimear regression and orthogonal polynomials, multiple regression, multiple and partial correlations, estimation of variance and covariance comp-onents, multivariate normal distribution Mahalanobis-D² and Hotelling’s T² statistics and their applications and properties, discriminant analysis canonical correlations,principal component analysis
IV Sampling Theory and Design of Experiments
An outline of fixed-population and super-population approaches, distinctive features of finite population sampling, probability sampling designs, simple random sampling with ad without replacement, stratified random sampling , systematic sampling and its efficacy, cluster sampling, two stage and multi-stage sampling, ratio and regression, methods of estimation involving one or more auxiliary variables,two-ohase sampling, probability proportional to size sampling with and without replacement, the Hansen-Hurwitz-Thompson estimators, non-negative variance estimation with reference to the Horvitz-Thompson estimator, non-sampling errors
Fixed effects model (two-way classification) ,random and mixed effects models(two-way classification withn equal observation per cell),CRD,RBD,LSD and their analyses,incomplete block designs,concepts of orthogonality and balance,BIBD,missing plot technique, factorial experiments and 2n and 3², confounding in factorial experiments,split-plot and simple lattice designs,transformation of data Duncan’s multiple range test.
PAPER-1
1 PROBABILITY
Sample space and events, probability mesure and probability space, random variable as a measurable function,distribution function of random variable, discrete and continuous type random variable, probability mass function, probability density function, vector-valued random variable, marginal and conditional distributions, stochastic independence of events and of random variables, exectation ad moments of random variable,conditional expectation , convergence of sequence of random variable in distribution, in probability ,in pth mean and lamost everywhere, their criteria and inter-relations Chebyshew’s inequality and Khintchine’s weak laws of large numbers, strong law of large numbers and Kolmogoroff’s theorems,probability generating function,moment generating function, characteristic function, inversion theorem, Linderberg and Levy forms of central limit theorem , standard discrete and continuous proability distributions.
II Statistical Inference
Consistency, unbiasedness, efficiency,cufficiency, completeness, ancillary statistics, factorization theorem, exponential family of distribution and its properties, uniformly minimum variance unbiased (UMVU) estimation,Rao-Backwell and Lehmann-Schefee theorems, Cramer-Rao inequality for single parameter:Estimation by methods of moments, maximum likelihood,least squares,minimum chi-square and modified minimum chi-square,properties of maximum likelihood and other estimator asymptotic efficiency,prior and posterior distribution ,loss function risk function risk function and minimax estimator Bayyes estimators
Non-randomised and randomized tests, critical function,MP tests,Neyman-Pearson lemma,UMP tests, monotone likelihood ratio,similar and unbiased tests,UMPU tests for single parameter likelihood ratio test its asymptotic distribution.Confidence bounds and its relation with tests.
Kolmogoroff’s test for goodness of fit and its consistency,sign test and its optimality.Wilcoxon signed-ranks test and its consistency,Kolmogorov two-sample test ,run test, Wilcoxon-Mann-Whitney test and median test, their consistency and asymptotic normality.
Wald’s SPRT and its properties,OC and ASN functions for tests regarding parameters for Bernoulli poisson, normal and exponential distribution .Wald’s fundamental identity
III.Linear Inference and Multivariate Analysis
Linear statistical models, theory of least squares and analysis of variance,Gauss-Markoff theory normal equations,least squares estimates and theior precision,test of significance and interval estimates based on least squares theory in one-way,two-way and three-way c;assified data,regression analysis linear regression , curvilimear regression and orthogonal polynomials, multiple regression, multiple and partial correlations, estimation of variance and covariance comp-onents, multivariate normal distribution Mahalanobis-D² and Hotelling’s T² statistics and their applications and properties, discriminant analysis canonical correlations,principal component analysis
IV Sampling Theory and Design of Experiments
An outline of fixed-population and super-population approaches, distinctive features of finite population sampling, probability sampling designs, simple random sampling with ad without replacement, stratified random sampling , systematic sampling and its efficacy, cluster sampling, two stage and multi-stage sampling, ratio and regression, methods of estimation involving one or more auxiliary variables,two-ohase sampling, probability proportional to size sampling with and without replacement, the Hansen-Hurwitz-Thompson estimators, non-negative variance estimation with reference to the Horvitz-Thompson estimator, non-sampling errors
Fixed effects model (two-way classification) ,random and mixed effects models(two-way classification withn equal observation per cell),CRD,RBD,LSD and their analyses,incomplete block designs,concepts of orthogonality and balance,BIBD,missing plot technique, factorial experiments and 2n and 3², confounding in factorial experiments,split-plot and simple lattice designs,transformation of data Duncan’s multiple range test.
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