{"id":9503,"date":"2026-02-18T16:34:18","date_gmt":"2026-02-18T11:04:18","guid":{"rendered":"https:\/\/vajiramandravi.com\/upsc-exam\/?p=9503"},"modified":"2026-02-20T10:37:12","modified_gmt":"2026-02-20T05:07:12","slug":"upsc-statistics-optional-syllabus","status":"publish","type":"post","link":"https:\/\/vajiramandravi.com\/upsc-exam\/upsc-statistics-optional-syllabus\/","title":{"rendered":"UPSC Statistics Optional Syllabus 2026 for CSE Mains Paper 1 & 2"},"content":{"rendered":"

Among the 48 optional subjects in the UPSC Exam, Statistics Optional is one of the least preferred due to its technical and specialized nature. Many candidates avoid it because of its mathematical concepts and challenging syllabus. However, for those with a solid understanding of probability, sampling, and data analysis, Statistics Optional can be a scoring subject with limited competition. This article covers the detailed UPSC Statistics Syllabus, link to download PDF, and other essential details.<\/span><\/p>\r\n

UPSC Statistics Syllabus<\/b><\/h2>\r\n

Statistics is a subject that includes collection, organization, analysis, interpretation, and presentation. Candidates with a strong interest in mathematical subjects and a preference for technical concepts may find Statistics Optional a suitable choice. The UPSC Statistics Syllabus is often aligned with topics covered in related graduation. Like other optional subjects, it consists of two papers, Paper 1 and Paper 2, each carrying 250 marks. With a clear understanding of the core concepts, candidates can score well in this subject.<\/span><\/p>\r\n

UPSC Statistics Syllabus for Paper 1<\/b><\/h2>\r\n

The UPSC Statistics Syllabus for Paper 1 includes the topics which are theoretical and fundamental concepts of statistics. For a detailed subject description, refer to the table below.<\/span><\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
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UPSC Statistics Syllabus for Paper 1<\/b><\/p>\r\n<\/td>\r\n<\/tr>\r\n

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Topic<\/span><\/p>\r\n<\/td>\r\n

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Subtopics<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

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Probability<\/span><\/p>\r\n<\/td>\r\n

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  • Sample space and events , probability measure and probability space, random variable as a measurable function.<\/span><\/li>\r\n\t
  • 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 moments of a random variable, conditional expectation, convergence of a sequence of random variable in distribution, in probability, in path mean and almost everywhere, their criteria and inter-relations, Chebyshev\u2019s inequality and Khintchine\u2019s weak law of large numbers, strong law of large numbers, and Kolmogoroffs theorems, probability generating function, moment generating function, characteristic function, inversion theorem, Lindenberg and Levy forms of central limit theorem, standard discrete and continuous probability distributions.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
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Statistical Inference<\/span><\/p>\r\n<\/td>\r\n

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  • Consistency, unbiasedness, efficiency , sufficiency, completeness, ancillary statistics, factorization theorem, exponential family of distribution and its properties, uniformly minimum variance unbiased ( UMVU ) estimation, Rao Blackwell and Lehmann-Scheffe theorem s, Cramer-Rao inequality for single Parameter.<\/span><\/li>\r\n<\/ul>\r\n
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    • Estimation by methods of moments, maximum likelihood, least squares, minimum chi-square and modified minimum chi-square, properties of maximum likelihood and other estimators, asymptotic efficiency, prior and posterior distributions, loss function, risk function, and minimax estimator. Bayes estimators.<\/span><\/li>\r\n<\/ul>\r\n
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      • Non-randomised and randomised 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 and its asymptotic distribution. Confidence bounds and its relation with tests.<\/span><\/li>\r\n<\/ul>\r\n
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        • Kolmogorov\u2019s test for goodness of fit and its consistency, sign test, and its optimality. Wilcoxon signed ranks test and its consistency, Kolmogorov-Smirnov two sample test, run test, Wilcoxon-Mann-Whitney test and median test, their consistency, and asymptotic normality.<\/span><\/li>\r\n<\/ul>\r\n
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          • Wald\u2019s SPRT and its properties, Oc, and ASN functions for tests regarding parameters for Bernoulli, Poisson, normal, and exponential distributions. Wald\u2019s fundamental identity.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
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Linear Inference and Multivariate Analysis<\/span><\/p>\r\n<\/td>\r\n

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  • Linear statistical models , theory of least squares and analysis of variance, Gauss-Markoff theorem, normal equations, least squares estimates, and their precision, test of significance, and interval estimates based on least squares theory in one way, two-way, and three-way classified data, regression analysis, linear regression, curvilinear regression, and orthogonal polynomials, multiple regression, multiple and partial correlations, estimation of variance and covariance components, multivariate normal distribution, Mahalanobis\u2019s D2 and Hotelling\u2019s T2 statistics and their applications and properties, discriminant analysis, canonical correlations, and principal component analysis.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
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Sampling Theory and Design of Experiments<\/span><\/p>\r\n<\/td>\r\n

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  • An outline of fixed-population and super-population approaches , distinctive features of finite population sampling, probability sampling designs, simple random sampling with and 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-phase sampling, probability proportional to size sampling with and without replacement, the Hansen-Hurwitz and the Horvitz Thompson estimators, non-negative variance estimation with reference to the Horvitz-Thompson estimator, non-sampling errors.<\/span><\/li>\r\n<\/ul>\r\n
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    • Fixed effects model (two-way classification) random and mixed effects models (two-way classification with 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 24 and 32, confounding in factorial experiments, split-plot and simple lattice designs, transformation of data Duncan\u2019s multiple range test.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

      UPSC Statistics Syllabus for Paper 2<\/b><\/h2>\r\n

      The UPSC Statistics Syllabus for Paper 2 includes the topics like official statistics, demography, and psychometry. For a detailed subject description, refer to the table below.<\/span><\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
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      UPSC Statistics Syllabus for Paper 2<\/b><\/p>\r\n<\/td>\r\n<\/tr>\r\n

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      Topic<\/span><\/p>\r\n<\/td>\r\n

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      Subtopics<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

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      Industrial Statistics<\/span><\/p>\r\n<\/td>\r\n

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      • Process and product control , general theory of control charts, different types of control charts for variables and attributes, X, R, s, p, np and charts, cumulative sum charts. Single, double, multiple, and sequential sampling plans for attributes, OC, ASN, AOQ, and ATI curves, concepts of producers and consumer\u2019s risks, AQL, LTPD, and AOQL, Sampling plans for variables, Use of Dodge-Romin tables.<\/span><\/li>\r\n\t
      • Concept of reliability , failure rate, and reliability functions, reliability of series and parallel systems and other simple configurations, renewal density, and renewal function, Failure models : exponential, Weibull, normal, lognormal. Problems in life testing censored and truncated experiments for exponential models.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
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      Optimization Techniques<\/span><\/p>\r\n<\/td>\r\n

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      • Different types of models in Operations Research , their construction, and general methods of solution, simulation and Monte-Carlo methods formulation of Linear Programming (LP) problem, simple LP model and its graphical solution, the simplex procedure, the two-phase method, and the M-technique with artificial variables, the duality theory of LP and its economic interpretation, sensitivity analysis, transportation and assignment problems, rectangular games, two-person zero sum games, methods of solution (graphical and algebraic).<\/span><\/li>\r\n\t
      • Replacement of failing or deteriorating items, group and individual replacement policies, the concept of scientific inventory management and analytical structure of inventory problems, simple models with deterministic and stochastic demand with and without lead time, storage models with particular reference to dam type.<\/span><\/li>\r\n\t
      • Homogeneous discrete-time Markov chains , transition probability matrix, classification of states, and ergodic theorems, homogeneous continuous-time Markov chains, Poisson process, elements of queuing theory, M\/MI, M\/M\/K, G\/M\/l and M\/G\/1 queues.<\/span><\/li>\r\n\t
      • Solution of statistical problems on computers using well-known statistical software packages like SPSS.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
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      Quantitative Economics and Official Statistics<\/span><\/p>\r\n<\/td>\r\n

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      • Determination of trend, seasonal, and cyclical components, Box-Jenkins method, tests for stationary series, ARIMA models, and determination of orders of autoregressive and moving average components, forecasting. Commonly used index numbers - Laspeyres, Paasche\u2019s, and Fisher\u2019s ideal index numbers, cham-base index number, uses and limitations of index numbers, the index number of wholesale prices, consumer prices, agricultural production, and industrial production, test for index numbers -proportionality, time-reversal, factor-reversal and circular.<\/span><\/li>\r\n\t
      • General linear model, ordinary least square and generalized least squares methods of estimation, the problem of multicollinearity, consequences, and solutions of multicollinearity, autocorrelation, and its consequences, heteroscedasticity of disturbances and its testing, test for independence of disturbances concept of structure and model for simultaneous equations, the problem of identification-rank and order conditions of identifiability, two-stage least square method of estimation.<\/span><\/li>\r\n\t
      • Present official statistical system in India relating to population, agriculture, industrial production, trade and prices, methods of collection of official statistics, their reliability and limitations, principal publications containing such statistics, various official agencies responsible for data collection, and their main functions.<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
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      Demography and Psychometry<\/span><\/p>\r\n<\/td>\r\n

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