OPTIONAL : STATISTICS
Syllabus:
Statistics Syllabus Paper – I
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 continuoustype random variable, probability mass function, probability density function, vectorvalued 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 a random variable in distribution, in probability, in pth mean and almost everywhere, their criteria and interrelations.
Chebyshev’s inequality and Khintchine‘s weak law 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 probability distributions.
2. Statistical Inference:
Consistency, unbiasedness, efficiency, sufficiency, completeness, ancillary statistics, factorization theorem, exponential family of distribution and its properties, uniformly minimum variance unbiased (UMVU) estimation, RaoBlackwell and LehmannScheffe theorems, CramerRao inequality for a 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. Nonrandomised and randomised tests, critical function, MP tests, NeymanPearson 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 to tests. Kolmogoroff’s test for goodness of fit and its consistency, sign test, and its optimality.
Wilcoxon signedranks test and its consistency, KolmogorovSmirnov twosample test, run test, WilcoxonMannWhitney 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.
3. Linear Inference and Multivariate Analysis:
Linear statistical models’, the theory of least squares and analysis of variance, GaussMarkoff theory, normal equations, least squares estimates and their precision, the test of significance and interval estimates based on least squares theory in oneway, twoway and threeway 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, MahalanobisD2 and Hotelling’s T2 statistics and their applications and properties, discriminant analysis, canonical correlations, principal component analysis.
4. Sampling Theory and Design of Experiments:
An outline of fixedpopulation 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 multistage sampling, ratio and regression methods of estimation involving one or more auxiliary variables, twophase sampling, probability proportional to size sampling with and without replacement, the HansenHurwitz and the HorvitzThompson estimators, nonnegative variance estimation with reference to the HorvitzThompson estimator, nonsampling errors.
Fixed effects model (twoway classification) random and mixed effects models (twoway 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 2n and 32, confounding in factorial experiments, splitplot and simple lattice designs, the transformation of data Duncan’s multiple range test.
Statistics Syllabus Paper – II
1. Industrial Statistics:
Process and product control, the general theory of control charts, different types of control charts for variables and attributes, X, R, s, p, np and c 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 DodgeRoaming tables.
The concept of reliability, failure rate and reliability functions, the 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.
2. 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 twophase method and the Mtechnique with artificial variables, the duality theory of LP and its economic interpretation, sensitivity analysis, transportation and assignment problems, rectangular games, twoperson zerosum games, methods of solution (graphical and algebraic).
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.
Homogeneous discretetime Markov chains, transition probability matrix, classification of states and ergodic theorems, homogeneous continuoustime Markov chains, Poisson process, elements of queuing theory, M/M/1, M/M/K, G/M/1 and M/G/1 queues. The solution of statistical problems on computers using wellknown statistical software packages like SPSS.
3. Quantitative Economics and Official Statistics:
Determination of trend, seasonal and cyclical components, BoxJenkins method, tests for stationary series, ARIMA models and determination of orders of autoregressive and moving average components, forecasting. Commonly used index numbers Laspeyres, Paasche’s and Fisher’s ideal index numbers, chainbase 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, timereversal, factorreversal and circular.
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, problem of identificationrank and order conditions of identifiability, twostage least square method of estimation. The 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.
4. Demography and Psychometry:
Demographic data from the 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, quasistable population, techniques in the estimation of demographic parameters, standard classification by cause of death, health surveys and use of hospital statistics. Methods of standardization of scales and tests, Zscores, standard scores, Tscores, 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.
Reference Books:
 An Introduction to Probability Theory & Mathematical Statistics V K Rohtagi
 Fundamentals of Statistics (2 Vol.) A M Goon, M K Gupta and B Dass Gupta
 Introductory Probability and Statistical Applications – Paul Meyer
 Sampling TechniquesWilliam G. Cochran
 Sampling Theory of Surveys with applications – B. V Sukhatme & B V Sukhatme
 An Outline of Statistical Theory (2 Vol.) A M Goon, M K Gupta and B .Dass Gupta
 Fundamentals of Mathematical StatisticsA C Gupta and V K Kapoor
 Fundamentals of Applied StatisticsS C Gupta and V K Kapoor
Strategy:
MERITS:
 This optional is fully problems and theorems oriented.
 One who has a background in statistics can really score high
Demerits:
 the syllabus of statistics for UPSC IAS Mains exam includes varied elements.
 The aspirants need to do intensive practicing and wide reading for preparing this paper.
How to prepare:
 Memorise the Syllabus.
 Stick to limited reference books
 Before starting preparation, go through previous year qps
 Based on previous qps analysis , make note of important topics
 Stress more on to the important topics.
 Prepare crispy notes, and learn formulas.
 Practise practise practise, this will help you.
 Solve previous year question papers at least 10 years.
Previous Year Question Papers:
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