Statistics Optional

**STATISTICS **

**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 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 interrelations, 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.

**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 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.

**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, 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.

**4. 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 Horvitz-Thompson 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 ob-servation per cell), CRD, RBD, LSD and their analyses, incom-plete 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.

**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 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 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, 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.

**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.

**How to prepare for statistics optional for IAS?**

Statistics optional is a branch of mathematics that basically deals in the collection, interpretation, and analysis of data. Statistics deal with all aspects of data like planning of data and collection of data for that matter. If a candidate studies this optional subject with the right approach then he/she can definitely score well. To help you further here are some tips that can be included during the preparation.

1. Before preparing for any competitive exam, it is advisable to know the syllabus of the exam. If you are well versed in the syllabus, you know what to study. Also through this, a candidate also gets to know which all are the topics at which he is good and which one are the topics at which he is not so good. So a basic understanding of the syllabus will be advantageous to identify strengths and weaknesses. So understanding the syllabus gives you a direction in which you need to work.

2. After knowing what to study and from where to study let's come to the point of how to study. It is better to make a study plan for yourself. This will help in time management and to study in a better way. Through this, you can allocate different time to different topics and decide at what time you will study what. It will save a lot of time and avoid unnecessary time wastage. In this way, saved time can be further utilized to study other general studies paper.

3. Candidates should have a basic understanding of all the concepts of the statistics. Also, each topic should be studied in depth in order to acquire a clear understanding. This will also help to solve questions easily and to give proper answers to the questions. In addition to this use flowcharts and diagrams while answering the questions. It helps to fetch good marks in the main exam.

4. Also, prepare notes. These notes help in the revision of the entire syllabus during the time of the exam. They boost a candidate’s score in the main exam since he/she need not rush behind multiple reference books. Instead of this, they can simply refer to their study notes which were made during the time of preparation.

5. One of the most crucial aspects of UPSC preparation is to solve past year papers of the optional subject. Most of the questions asked in animal husbandry and veterinary science are from past year paper. These questions are also straightforward. So it is most essential aspect to solve past year papers. This will help to score better marks.

6. It is very important to thoroughly study the whole syllabus of statistics optional twice and thrice. And then keep on revising it as many times as possible. Revision helps to absorb the things in a better way. It helps to keep the whole of the syllabus in our brain for a longer duration.

If a student keeps on learning and doesn’t revise what he has studied then he tends to forget the thing on the day of the exam. This is because what he/she studies didn’t ever get registered in his brain. Thus revision is the key factor to restore things in the brain.

7. Most of the students are unable to manage the time during the exam. This happens because many times a candidate spends a lot of time thinking about an answer to particular questions and this leads to a lot of wastage of time. Instead of this one needs to specify and allocate proper time to each and every question. It will help to finish the paper on time. Also, time management is important to avoid any last-minute hassle. When less time is left and there are more questions left to be answered then many times a candidate marks a wrong answer even if he/she knows the correct answer.

8. Confidence helps to boost your morale during the preparation. It helps to overcome stress which every candidate tends to face every day. Since IAS exam preparation is not also easy, so many times candidate feels to give up. But by being confident you can easily overcome the stress and the negative thoughts that occupy your mind. It helps in concentration and you are able to focus more on your studies well. It helps you to remain calm and composed throughout your preparation.

9. The next key aspect to keep in mind during preparation is to practice the mock test papers. Practicing mock test papers will give you a real-time analysis through which you get an idea of how the final paper will come. This will also help to practice different types of questions. A variety of questions helps to solve all types of questions during the final exam. In addition to this make notes of the subject. Try to summarize the topic in notes format. These notes will act as a guiding light during the last phase of the preparation and help you to crack the exam. Also if you have notes then you don’t need to refer other fat books.