UPSC IAS Statistics Optional Syllabus for Paper I and Paper II

The UPSC optional syllabus of Statistics consists of two papers, Paper I and Paper II, each carrying a weightage of 250 marks. Both the papers are divided into different sections, and candidates have to choose one subject from each section. Let us look into the details of each paper.

UPSC Statistics Optional Syllabus

UPSC Statistics syllabus includes topics like probability theory, sampling theory, estimation and quantitative economics. Candidates who want to choose Statistics as optional for UPSC Mains must be familiar with the UPSC Statistics syllabus.

By combining excellent methods with rigorous study, candidates will be able to cover the Statistics optional course with ease. Many applicants believe that statistics is similar to mathematics, however, this is not the case. UPSC Statistics syllabus can be highly interesting if studied properly.

UPSC Statistics Syllabus	Topics
Paper I	Probability Statistical Inference Linear Inference and Multivariate Analysis Sampling Theory and Design of Experiments
Paper II	Industrial Statistics Optimization Techniques Quantitative Economics and Official Statistics Demography and Psychometry

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UPSC Statistics Optional Syllabus for Paper I

1. Probability

Sample space and events, probability measure and probability space, random variable as a measurable function. the 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 random variables, expectation and moments of a random variable, conditional expectation, convergence of a sequence of the 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 the 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, Rao Blackwell and Lehmann-Scheffe 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 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 parameter 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 signed-ranks test and its consistency, Kolmogorov-Smirnov two-sample test, run test, Wilcoxon-MannWhitney 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, theory of least squares and analysis of variance, Gauss-Markoff theory, normal equations, least squares estimates and their precision, a 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, and principal component analysis.

4. 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 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 HorvitzThompson estimators, non-negative variance estimation about 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.

UPSC Statistics Optional Syllabus for Paper II

1. 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.

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 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).
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 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 well-known statistical software packages like SPSS.

3. 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, forecasting.
Commonly used index numbers – Laspeyre’s, Paasche’s and Fisher’s ideal index numbers, cham-base index number, uses and limitations of index numbers, the index number of wholesale prices, consumer price, agricultural production and industrial production, test for index numbers -proportionality, time-reversal, factor-reversal and circular.
General linear model, ordinary least square and generalized least squares methods of estimation, the 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, the problem of identification-rank and order conditions of identifiability, two-stage least square 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.

4. 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.

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Tips to Prepare for UPSC Statistics Syllabus

Understand the Syllabus Thoroughly: The first and most important step is to understand the UPSC Statistics syllabus thoroughly. Make sure you are familiar with all the topics covered in both Paper I and Paper II. You can find the syllabus on the UPSC website.
Prepare a Study Plan: Once you understand the syllabus, it is important to prepare a study plan. This will help you stay on track and ensure you cover all the essential topics. Your study plan should be realistic and achievable given the time you have available.
Practice solving previous years’ question papers: The best way to prepare for UPSC Statistics Optional is to practice solving previous years’ question papers. This will help you become familiar with the types of questions asked and develop problem-solving skills.
Join a coaching class or online course (optional): If you feel you need some extra help, you may consider joining a coaching class or online course. This can be a good way to get additional guidance and support from experienced teachers.
Stay Motivated: Preparing for UPSC Statistics Optional can be a challenging task. It is important to stay motivated during your preparation. One way to do this is to set realistic goals and track your progress. You can also reward yourself for meeting your goals.

Additional Tips:

Make sure you understand the concepts behind the formulas.
Don’t be afraid to ask for assistance if you need it.
Take breaks and avoid burnout.
Have faith in yourself and your ability to succeed.

I hope these tips will help you in preparing for the UPSC Statistics course. Remember, hard work and dedication are the key to success in this exam.