UPSC CSE Statistics Optional Syllabus 2021
By On June 5th, 2021
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UPSC CSE Statistics Optional Syllabus for Paper-I, UPSC CSE Statistics Optional Syllabus for Paper-II upsc statistics optional question paper, upsc statistics optional paper, upsc statistics optional toppers, upsc optional syllabus, upsc statistics optional books, upsc statistics optional notes, upsc mains syllabus, highest marks in statistics optional upsc
UPSC CSE Statistics Optional Syllabus for Paper-I
  • 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 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’s inequality and Khintchine’s weak law of large
    numbers, strong law of large numbers and Kolmogoroffs theorems, probability generating
    function, moment generating function, characteristic function, inversion theorem, Linderberg and
    Levy forms of central limit theorem, standard discrete and continuous probability distributions.
  • Statistical Inference:
    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 theorems, Cramer-Rao
    inequality for single Parameter. Estimation by methods of moments, maximum likelihood, least
    squares, minimum chisquare and modified minimum chisquare, properties of maximum likelihood
    and other estimators, asymptotic efficiency, prior and posterior distributions, loss function, risk
    function, and minimax estimator. Bayes estimators.
    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 paramet
    likelihood ratio test and its asymptotic distribution. Confidence bounds and its relation with tests.
    Kolmogorov’s test for goodness of fit and its consistency, sign test and its optimality. Wilcoxon
    signedranks test and its consistency, Kolmogorov-Smirnov 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 distributions. Wald’s fundamental identity.
  • 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 their precision, test of significance and
    interval estimates based on least squares theory in oneway, 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’s D2 and Hotelling’s T2 statistics and their
    applications and properties, discriminant analysis, canonical correlations, principal component
    analysis.
  • Sampling Theory and Design of Experiments :
    An outline of fixed-population and super-population approaches, distinctive features of finite
    population sampling, propability sampling designs, simple random sampling with and without
    replacement, stratified random sampling, systematic sampling and its efficacy, cluster sampling,
    twostage 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 HorvitzThompson 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 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’s multiple range test.
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UPSC CSE Statistics Optional Syllabus for Paper-II
  • Industrial Statistics
    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 chart. Single, double,
    multiple and sequential sampling plans for attributes, OC, ASN, AOQ and ATI curves, concepts of
    producer’s and consumer’s risks, AQL, LTPD and AOQL, Sampling plans for variables, Use of
    Dodge-Romin tables.
    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.
  • Optimization Techniques :
    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 metbod and the
    M-technique with artificial variables, the duality theory of LP and its economic interpretation,
    sensitivity analysis, transpotation and assignment problems, rectangular games, two-person zerosum games, methods of solution (graphical and algebraic).
    Replacement of failing or deteriorating items, group and individual replacement policies,
    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.
    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.
    Solution of statistical problems on computers using wellknown statistical software packages
    like SPSS.
  • Quantitative Economics and Official Statistics:
    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, fore-casting.
    Commonly used index numbers – Laspeyre’s, Paasche’s and Fisher’s ideal index numbers,
    cham-base index number, uses and limitations of index numbers, index number of wholesale
    prices, consumer price, agricultural production and industrial production, test fot index numbers
    -proportionality, time-reversal, factor-reversal and circular.
    General linear model, ordinary least square and generalized least squares methods of
    estimation, problem of multi-collinearity, consequences and solutions of multi-collinearity,
    autocorrelation and its consequences, heteroscedasticity of disturbances and its testing, test for
    independence of disturbances concept of structure and model for simultaneous equations,
    problem of identification-rank and order conditions of identifiability, two-stage least sauare
    method of estimation.
    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.
  • Demography and Psychometry :
    Demographic data from census, registration, NSS other surveys, their limitations. and uses,
    definition, construction and uses of vital rates and ratios, measures of fertility, reproduction rates,
    morbidity rate, standardized death rate, complete and abridged life tables, construction of life
    tables from vital statistics and census returns, uses of life tables, logistic and other population
    growth curves, fitting a logistic curve, population projection, stable population, quasi-stable
    population, techniques in estimation of demographic parameters, standard classification by cause
    of death, health surveys and use of hospital statistics.
    Methods of standardisation of scales and tests, Z-scores, standard scores, T-scores, percentile
    scores, intelligence quotient and its measurement and uses, validity and reliability of test scores
    and its determination, use of factor analysis and path analysis in psychometry.

Frequently Asked Questions (FAQs) On UPSC CSE Optional Syllabus 

Question- What is the UPSC’s Annual Programme (Calendar) of Examinations/RTs (Recruitment Tests)?
Answer – The UPSC publishes an Annual Programme (Calendar) of all the Structured Examinations/RTs conducted by it at least 6 months in advance (i.e. in June) for the Examinations/RTs to be conducted during the next calendar year. The Programme is uploaded on the UPSC’s website as also published in the leading news papers of the country. The date of issue of Examination Notice for each Examination is also mentioned in this Annual Programme.

Question- What happens if a candidate submits multiple online applications?
Answer – While a candidate should avoid submitting more than one online application, in case of doing so, the data provided in the last application (highest RID Number), that is successfully submitted online, is accepted by the Commission. All previous applications are ignored as these are amalgamated with the last completed & finally submitted application. If an applicant (who has already submitted an application successfully) wants to
make amendments in the application, then he has to submit a fresh application on or before the last date of submission of application of the Examination. Therefore, it must be ensured that fee is submitted against the
last online application only, which should also be complete in all respects including its final submission. Fee paid against one RID shall not be adjusted against any other RID number

Question- What action is taken by the Commission in case of submission of false information by the candidates?
Answer – A candidate found to be furnishing false information to the Commission or suppressing information, adopting various unfair means in the Examination like impersonation, cheating, etc., is liable to be disqualified
and/or debarred from writing UPSC Examinations as decided by the Commission. A detailed stipulation in this regard is incorporated in the Rules of Examination/ Examination Notices.

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