{"id":96921,"date":"2021-03-20T19:38:16","date_gmt":"2021-03-20T14:08:16","guid":{"rendered":"https:\/\/blog.forumias.com\/?page_id=96921"},"modified":"2023-10-26T18:01:28","modified_gmt":"2023-10-26T12:31:28","slug":"statistics-syllabus","status":"publish","type":"page","link":"https:\/\/forumias.com\/blog\/upsc-syllabus\/statistics-syllabus\/","title":{"rendered":"Statistics Optional UPSC Syllabus"},"content":{"rendered":"

Statistics Optional-Syllabus\u00a0<\/strong><\/p>\n

PAPER\u2013I<\/h5>\n

1. Probability :<\/strong>
\nSample space and events, probability measure and probability space, random variable as a
\nmeasurable function.
\ndistribution function of a random variable, discrete and continuous-type random variable,
\nprobability mass function, probability density function, vector-valued random variable, marginal and conditional distributions, stochastic independence of events and of random variables,
\nexpectation and moments of a random variable, conditional expectation, convergence of a
\nsequence of random variable in distribution, in probability, in path mean and almost everywhere,
\ntheir criteria and inter-relations, Chebyshev\u2019s inequality and Khintchine\u2019s weak law of large
\nnumbers, strong law of large numbers and Kolmogoroffs theorems, probability generating
\nfunction, moment generating function, characteristic function, inversion theorem, Linderberg and
\nLevy forms of central limit theorem, standard discrete and continuous probability distributions.<\/p>\n

2. Statistical Inference:<\/strong>
\nConsistency, unbiasedness, efficiency, sufficiency, completeness, ancillary statistics,
\nfactorization theorem, exponential family of distribution and its properties, uniformly minimum
\nvariance unbiased (UMVU) estimation, Rao Blackwell and Lehmann-Scheffe theorems, Cramer-Rao
\ninequality for single Parameter. Estimation by methods of moments, maximum likelihood, least
\nsquares, minimum chisquare and modified minimum chisquare, properties of maximum likelihood
\nand other estimators, asymptotic efficiency, prior and posterior distributions, loss function, risk
\nfunction, and minimax estimator. Bayes estimators.
\nNon-randomised and randomised tests, critical function, MP tests, Neyman-Pearson lemma,
\nUMP tests, monotone likelihood ratio: similar and unbiased tests, UMPU tests for single paramet
\nlikelihood ratio test and its asymptotic distribution. Confidence bounds and its relation with tests.
\nKolmogorov\u2019s test for goodness of fit and its consistency, sign test and its optimality. Wilcoxon
\nsignedranks test and its consistency, Kolmogorov-Smirnov two sample test, run test,
\nWilcoxon-Mann-Whitney test and median test, their consistency and asymptotic normality.
\nWald\u2019s SPRT and its properties, Oc and ASN functions for tests regarding parameters for
\nBernoulli, Poisson, normal and exponential distributions. Wald\u2019s fundamental identity.<\/p>\n

3. Linear Inference and Multivariate Analysis :<\/strong>
\nLinear statistical models, theory of least squares and analysis of variance, Gauss-Markoff
\ntheory, normal equations, least squares estimates and their precision, test of significance and
\ninterval estimates based on least squares theory in oneway, two-way and three-way classified data,
\nregression analysis, linear regression, curvilinear regression and orthogonal polynomials, multiple
\nregression, multiple and partial correlations, estimation of variance and covariance components,
\nmultivariate normal distribution, Mahalanobis\u2019s D2 and Hotelling\u2019s T2 statistics and their
\napplications and properties, discriminant analysis, canonical correlations, principal component
\nanalysis.<\/p>\n

4. Sampling Theory and Design of Experiments :<\/strong>
\nAn outline of fixed-population and super-population approaches, distinctive features of finite
\npopulation sampling, propability sampling designs, simple random sampling with and without
\nreplacement, stratified random sampling, systematic sampling and its efficacy, cluster sampling,
\ntwostage and multi-stage sampling, ratio and regression methods of estimation involving one or
\nmore auxiliary variables, two-phase sampling, probability proportional to size sampling with and
\nwithout replacement, the Hansen-Hurwitz and the HorvitzThompson estimators, non-negative
\nvariance estimation with reference to the Horvitz-Thompson estimator, non-sampling errors.
\nFixed effects model (two-way classification) random and mixed effects models (two-way
\nclassification with equal observation per cell), CRD, RBD, LSD and their analyses, incomplete block
\ndesigns, concepts of orthogonality and balance, BIBD, missing plot technique, factorial
\nexperiments and 24 and 32, confounding in factorial experiments, split-plot and simple lattice
\ndesigns, transformation of data Duncan\u2019s multiple range test.<\/p>\n

PAPER -II<\/h5>\n

1. Industrial Statistics<\/strong>
\nProcess and product control, general theory of control charts, different types of control charts
\nfor variables and attributes, X, R, s, p, np and charts, cumulative sum chart. Single, double,
\nmultiple and sequential sampling plans for attributes, OC, ASN, AOQ and ATI curves, concepts of
\nproducer\u2019s and consumer\u2019s risks, AQL, LTPD and AOQL, Sampling plans for variables, Use of
\nDodge-Romin tables.
\nConcept of reliability, failure rate and reliability functions, reliability of series and parallel
\nsystems and other simple configurations, renewal density and renewal function, Failure models:
\nexponential, Weibull, normal, lognormal. Problems in life testing, censored and truncated
\nexperiments for exponential models.<\/p>\n

2. Optimization Techniques :<\/strong>
\nDifferent types of models in Operations Research, their construction and general methods of
\nsolution,
\nsimulation and Monte-Carlo methods formulation of Linear Programming (LP) problem, simple LP
\nmodel and its graphical solution, the simplex procedure, the two-phase metbod and the
\nM-technique with artificial variables, the duality theory of LP and its economic interpretation,
\nsensitivity analysis, transpotation and assignment problems, rectangular games, two-person zero\u0002sum games, methods of solution (graphical and algebraic).
\nReplacement of failing or deteriorating items, group and individual replacement policies,
\nconcept of scientific inventory management and analytical structure of inventory problems, simple
\nmodels with deterministic and stochastic demand with and without lead time, storage models
\nwith particular reference to dam type.
\nHomogeneous discrete-time Markov chains, transition probability matrix, classification of
\nstates and ergodic theorems, homogeneous continuous-time Markov chains, Poisson process,
\nelements of queuing theory, M\/MI, M\/M\/K, G\/M\/l and M\/G\/1 queues.
\nSolution of statistical problems on computers using wellknown statistical software packages
\nlike SPSS.<\/p>\n

3. Quantitative Economics and Official Statistics:<\/strong>
\nDetermination of trend, seasonal and cyclical components, Box-Jenkins method, tests for
\nstationary series, ARIMA models and determination of orders of autoregressive and moving
\naverage components, fore-casting.
\nCommonly used index numbers – Laspeyre\u2019s, Paasche\u2019s and Fisher\u2019s ideal index numbers,
\ncham-base index number, uses and limitations of index numbers, index number of wholesale
\nprices, consumer price, agricultural production and industrial production, test fot index numbers
\n-proportionality, time-reversal, factor-reversal and circular.
\nGeneral linear model, ordinary least square and generalized least squares methods of
\nestimation, problem of multi-collinearity, consequences and solutions of multi-collinearity,
\nautocorrelation and its consequences, heteroscedasticity of disturbances and its testing, test for
\nindependence of disturbances concept of structure and model for simultaneous equations,
\nproblem of identification-rank and order conditions of identifiability, two-stage least sauare
\nmethod of estimation.
\nPresent official statistical system in India relating to population, agriculture, industrial
\nproduction, trade and prices, methods of collection of official statistics, their reliability and
\nlimitations, principal publications containing such statistics, various official agencies responsible
\nfor data collection and their main functions.<\/p>\n

4. Demography and Psychometry :<\/strong>
\nDemographic data from census, registration, NSS other surveys, their limitations. and uses,
\ndefinition, construction and uses of vital rates and ratios, measures of fertility, reproduction rates,
\nmorbidity rate, standardized death rate, complete and abridged life tables, construction of life
\ntables from vital statistics and census returns, uses of life tables, logistic and other population
\ngrowth curves, fitting a logistic curve, population projection, stable population, quasi-stable
\npopulation, techniques in estimation of demographic parameters, standard classification by cause
\nof death, health surveys and use of hospital statistics.
\nMethods of standardisation of scales and tests, Z-scores, standard scores, T-scores, percentile
\nscores, intelligence quotient and its measurement and uses, validity and reliability of test scores
\nand its determination, use of factor analysis and path analysis in psychometry.<\/p>\n","protected":false},"excerpt":{"rendered":"

Statistics Optional-Syllabus\u00a0 PAPER\u2013I 1. Probability : Sample space and events, probability measure and probability space, random variable as a measurable function. distribution function of a 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, expectation and… Continue reading Statistics Optional UPSC Syllabus<\/span><\/a><\/p>\n","protected":false},"author":61,"featured_media":0,"parent":50153,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"class_list":["post-96921","page","type-page","status-publish","hentry","entry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/forumias.com\/blog\/wp-json\/wp\/v2\/pages\/96921","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/forumias.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/forumias.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/forumias.com\/blog\/wp-json\/wp\/v2\/users\/61"}],"replies":[{"embeddable":true,"href":"https:\/\/forumias.com\/blog\/wp-json\/wp\/v2\/comments?post=96921"}],"version-history":[{"count":0,"href":"https:\/\/forumias.com\/blog\/wp-json\/wp\/v2\/pages\/96921\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/forumias.com\/blog\/wp-json\/wp\/v2\/pages\/50153"}],"wp:attachment":[{"href":"https:\/\/forumias.com\/blog\/wp-json\/wp\/v2\/media?parent=96921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}