A PREMIERE INSTITUTE FOR ISS, IIT JAM(MS), GATE(ST), RBI GROUP 'B' DRDSIM, & OTHER Exams Related to Statistics
INDIAN STATISTICAL SERVICE
ABOUT INDIAN STATISTICAL SERVICE(ISS) EXAM
The ISS along with Indian Economic Service (IES) was constituted as a GroupA Central Service on 1 November 1961 by a Gazette notification. All statistical posts of different ministries and departments were pooled together in the initial constitution of service. The objective of the creation of the service was institutionalizing a core professional capacity within the Government to consolidate and disseminate the statistics at the national and international level and render crucial statistical needs of planning, policy formulation, and decision making.
Age Limit: –

2130 years (Age relaxation is according to the category of the applicant).

A candidate must have attained the age of 21 years and must not have attained the age of 30 years on 1st August 2020 i.e he/she must have been born not earlier than 2nd August 1989 and not later than 1st August 1998.
Education Qualification: –

Bachelor’s degree in Statistics/Mathematical Statistics/Applied Statistics for Indian Statistical Service.

From a University incorporated by of an Act of the Central or State Legislature in India or other Educational Institutes established by an Act Parliament or declared to be deemed as University under Section 3 of the University Grants Commission Act, 1956 or a Foreign University approved by the Central Government from time to time.
Registration process:

Go to the official website of UPSC and fill the registration form (candidates should have their own valid mobile number and active Email ID).

Pay the Examination Fee

UR/GEN/OBC will be Rs. 200/

SC/ST/PH No Fee

SYLLABUS & EXAM PATTERN OF INDIAN STATISTICAL SERVICE EXAM
The examination shall be conducted according to the following plan—

Part IWritten examination carrying a maximum of 1000 marks in the subjects as shown below.

Part IIViva voce of such candidates as may be called by the Commission carrying a maximum of 200 marks.
PARTI
For the subjects of the written examination under PartI, the maximum marks allotted to each subject/paper and the time allowed shall be as follows:
STANDARD AND SYLLABI
The standard of papers in General English and General Studies will be such as may be expected of a graduate of an Indian University.
The standard of papers in the other subjects will be that of the Master’s degree examination of an Indian University in the relevant disciplines. The candidates will be expected to illustrate the theory by facts, and to analyze problems with the help of theory. They will be expected to be particularly conversant with Indian problems in the field(s) of Economics/Statistics.
GENERAL ENGLISH
Candidates will be required to write an essay in English. Other questions will be designed to test their understanding of English and workmanlike use of words. Passages will usually be set for summary or precis.
GENERAL STUDIES
General knowledge including knowledge of current events and of such matters of everyday observation and experience in their scientific aspects as may be expected of an educated person who has not made a special study of any scientific subject. The paper will also include questions on Indian Polity including the political system and the Constitution of India, History of India, and Geography of nature which a candidate should be able to answer without special study.
STATISTICSI (OBJECTIVE TYPE)
(i) Probability:
Classical and axiomatic definitions of Probability and consequences. Law of total probability, Conditional probability, Bayes' theorem, and applications. Discrete and continuous random variables. Distribution functions and their properties.
Standard discrete and continuous probability distributions  Bernoulli, Uniform, Binomial, Poisson, Geometric, Rectangular, Exponential, Normal, Cauchy, Hypergeometric, Multinomial, Laplace, Negative binomial, Beta, Gamma, Lognormal. Random vectors, Joint and marginal distributions, conditional distributions, Distributions of functions of random variables. Modes of convergences of sequences of random variables  in distribution, in probability, with probability one and in mean square. Mathematical expectation and conditional expectation. Characteristic function, moment and probability generating functions, Inversion, uniqueness, and continuity theorems. Borel 01 law, Kolmogorov's 01 law. Tchebycheff's and Kolmogorov's inequalities. Laws of large numbers and central limit theorems for independent variables.
(ii) Statistical Methods:
Collection, compilation, and presentation of data, charts, diagrams, and histogram. Frequency distribution. Measures of location, dispersion, skewness, and kurtosis. Bivariate and multivariate data. Association and contingency. Curve fitting and orthogonal polynomials. Bivariate normal distribution. Regressionlinear, polynomial. Distribution of the correlation coefficient, Partial and multiple correlations, Intraclass correlation, Correlation ratio.
Standard errors and large sample tests. Sampling distributions of sample mean, sample variance, t, chisquare, and F; tests of significance based on them, Small sample tests.
Nonparametric testsGoodness of fit, sign, median, run, Wilcoxon, MannWhitney, Wald Wolfowitz and KolmogorovSmirnov. Order statisticsminimum, maximum, range, and median. Concept of Asymptotic relative efficiency.
(iii) Numerical Analysis:
Finite differences of different orders: E and D operators, factorial representation of a polynomial, separation of symbols, subdivision of intervals, differences of zero.
Concept of interpolation and extrapolation: Newton Gregory's forward and backward interpolation formulae for equal intervals, divided differences and their properties, Newton's formula for divided difference, Lagrange’s formula for unequal intervals, central difference formula due to Gauss, Sterling, and Bessel, the concept of error terms in interpolation formula.
Inverse interpolation: Different methods of inverse interpolation.
Numerical differentiation: Trapezoidal, Simpson’s onethird, and threeeight rule, and Waddle's rule.
Summation of Series: Whose general term (i) is the first difference of a function (ii) is in geometric progression.
Numerical solutions of differential equations: Euler's Method, Milne’s Method, Picard’s Method, and RungeKutta Method.
(iv) Computer application and Data Processing:
Basics of Computer: Operations of a computer, Different units of a computer system like central processing unit, memory unit, arithmetic and logical unit, an input unit, output unit, etc., Hardware including different types of input, output and peripheral devices, Software, system and application software, number systems, Operating systems, packages and utilities, Low and Highlevel languages, Compiler, Assembler, Memory – RAM, ROM, unit of computer memory (bits, bytes, etc.), Network – LAN, WAN, internet, intranet, basics of computer security, virus, antivirus, firewall, spyware, malware, etc.
Basics of Programming: Algorithm, Flowchart, Data, Information, Database, an overview of different programming languages, frontend and backend of a project, variables, control structures, arrays, and their usages, functions, modules, loops, conditional statements, exceptions, debugging and related concepts.
STATISTICS II (OBJECTIVE TYPE)
(i) Linear Models:
Theory of linear estimation, GaussMarkov linear models, estimable functions, error and estimation space, normal equations and least square estimators, estimation of error variance, estimation with correlated observations, properties of least square estimators, the generalized inverse of a matrix, and solution of normal equations, variances, and covariances of least square estimators.
Oneway and twoway classifications, fixed, random, and mixedeffects models. Analysis of variance (twoway classification only), multiple comparison tests due to Tukey, Scheffe, and StudentNewmannKeulDuncan.
(ii) Statistical Inference and Hypothesis Testing:
Characteristics of a good estimator. Estimation methods of maximum likelihood, minimum chisquare, moments, and least squares. Optimal properties of maximum likelihood estimators. Minimum variance unbiased estimators. Minimum variance bound estimators. CramerRao inequality. Bhattacharya bounds. Sufficient estimator. Factorization theorem. Complete statistics. RaoBlackwell theorem. Confidence interval estimation. Optimum confidence bounds. Resampling, Bootstrap, and Jackknife.
Hypothesis testing: Simple and composite hypotheses. Two kinds of error. Critical region. Different types of critical regions and similar regions. Power function. Most powerful and uniformly most powerful tests. NeymanPearson fundamental lemma. Unbiased test. Randomized test. Likelihood ratio test. Wald's SPRT, OC, and ASN functions. Elements of decision theory.
(iii) Official Statistics:
National and International official statistical system
Official Statistics: (a) Need, Uses, Users, Reliability, Relevance, Limitations, Transparency, its visibility (b) Compilation, Collection, Processing, Analysis and Dissemination, Agencies Involved, Methods
National Statistical Organization: Vision and Mission, NSSO and CSO; roles and responsibilities; Important activities, Publications, etc.
National Statistical Commission: Need, Constitution, its role, functions, etc.; Legal Acts/ Provisions/ Support for Official Statistics; Important Acts
Index Numbers: Different Types, Need, Data Collection Mechanism, Periodicity, Agencies Involved, Uses
Sector Wise Statistics: Agriculture, Health, Education, Women, and Child, etc. Important
Surveys & Census, Indicators, Agencies, and Usages, etc.
National Accounts: Definition, Basic Concepts; issues; the Strategy, Collection of Data and Release.
Population Census: Need, Data Collected, Periodicity, Methods of data collection, dissemination, Agencies involved.
Misc.: SocioEconomic Indicators, Gender Awareness/Statistics, Important Surveys, and Censuses.
STATISTICS III (DESCRIPTIVE TYPE)
(i) Sampling Techniques:
Concept of population and sample, need for sampling, complete enumeration versus sampling, basic concepts in sampling, sampling and Nonsampling error, Methodologies in sample surveys (questionnaires, sampling design, and methods followed in field investigation) by NSSO.
Subjective or purposive sampling, probability sampling or random sampling, simple random sampling with and without replacement, estimation of population mean, population proportions, and their standard errors. Stratified random sampling, proportional and optimum allocation, comparison with simple random sampling for fixed sample size. Covariance and Variance Function.
Ratio, product and regression methods of estimation, estimation of population mean, evaluation of Bias and Variance to the first order of approximation, comparison with simple random sampling. Systematic sampling (when population size (N) is an integer multiple of sampling size (n)). Estimation of population mean and standard error of this estimate, comparison with simple random sampling. Sampling with probability proportional to size (with and without replacement method), Des Raj and Das estimators for n=2, Horvitz Thomson’s estimator Equal size cluster sampling: estimators of population mean and total and their standard errors, comparison of cluster sampling with SRS in terms of an intraclass correlation coefficient. Concept of multistage sampling and its application, twostage sampling with an equal number of second stage units, estimation of population mean and total. Double sampling in ratio and regression methods of estimation. Concept of interpenetrating subsampling.
(ii) Econometrics:
Nature of econometrics, the general linear model (GLM) and its extensions, ordinary least squares (OLS) estimation and prediction, generalized least squares (GLS) estimation and prediction, heteroscedastic disturbances, pure and mixed estimation.
Autocorrelation, its consequences, and tests. Theil BLUS procedure, estimation, and prediction, multicollinearity problem, its implications and tools for handling the problem, ridge regression.
Linear regression and stochastic regression, instrumental variable estimation, errors in variables, autoregressive linear regression, lagged variables, distributed lag models, estimation of lags by OLS method, Koyck’s geometric lag model.
Simultaneous linear equations model and its generalization, identification problem, restrictions on structural parameters, rank and order conditions.
Estimation in simultaneous equations model, recursive systems, 2 SLS estimators, limited information estimators, kclass estimators, 3 SLS estimator, full information maximum likelihood method, prediction, and simultaneous confidence intervals.
(iii) Applied Statistics:
Index Numbers: Price relatives and quantity or volume relatives, Link and chain relatives
composition of index numbers; Laspeyre's, Paasches’, Marshal Edgeworth and Fisher index numbers; chain base index number, tests for index number, Construction of index numbers of wholesale and consumer prices, Income distributionPareto, and Engel curves, Concentration curve, Methods of estimating national income, Intersectoral flows, Interindustry table, Role of CSO. Demand Analysis
Time Series Analysis: Economic time series, different components, illustration, additive and multiplicative models, determination of trend, seasonal and cyclical fluctuations.
Timeseries as discrete parameter stochastic process, autocovariance and autocorrelation functions, and their properties.
Exploratory time Series analysis, tests for trend and seasonality, exponential and moving average smoothing. Holt and Winters smoothing, forecasting based on smoothing.
A detailed study of the stationary processes: (1) moving average (MA), (2) autoregressive (AR), (3) ARMA, and (4) AR integrated MA (ARIMA) models. BoxJenkins models, choice of AR, and MA periods.
Discussion (without proof) of estimation of mean, autocovariance, and autocorrelation functions under large sample theory, estimation of ARIMA model parameters.
STATISTICSIV (DESCRIPTIVE TYPE)
(i) Operations Research and Reliability:
Definition and Scope of Operations Research: phases in Operation Research, models and their solutions, decisionmaking under uncertainty and risk, use of different criteria, sensitivity analysis.
Transportation and assignment problems. Bellman’s principle of optimality, general formulation, computational methods, and application of dynamic programming to LPP.
Decisionmaking in the face of competition, twoperson games, pure and mixed strategies, the existence of solution and uniqueness of value in zerosum games, finding solutions in 2x2, 2xm, and mxn games.
Analytical structure of inventory problems, EOQ formula of Harris, its sensitivity analysis, and extensions allowing quantity discounts and shortages. Multiitem inventory subject to constraints. Models with random demand, the static risk model. P and Q systems with constant and random lead times.
Queuing models – specification and effectiveness measures. Steadystate solutions of M/M/1 and M/M/c models with associated distributions of queuelength and waiting time. M/G/1 queue and PollazcekKhinchine result.
Sequencing and scheduling problems. 2machine njob and 3machine njob problems with identical machine sequence for all jobs
Branch and Bound method for solving traveling salesman problem.
Replacement problems – Block and age replacement policies.
PERT and CPM – basic concepts. Probability of project completion.
Reliability concepts and measures, components and systems, coherent systems, reliability of coherent systems. Lifedistributions, reliability function, hazard rate, common univariate life distributions – exponential, Weibull, gamma, etc. Bivariate exponential distributions.
Estimation of parameters and tests in these models.
Notions of aging – IFR, IFRA, NBU, DMRL, and NBUE classes and their duals. Loss of memory property of the exponential distribution.
Reliability estimation based on failure times in variously censored lifetests and in tests with the replacement of failed items. Stressstrength reliability and its estimation.
(ii) Demography and Vital Statistics:
Sources of demographic data, census, registration, adhoc surveys, Hospital records, Demographic profiles of the Indian Census.
Complete life table and its main features, Uses of life table. Markham's and Gompertz's curves. National life tables. UN model life tables. Abridged life tables. Stable and stationary populations.
Measurement of Fertility: Crude birth rate, General fertility rate, Agespecific birth rate, Total fertility rate, Gross reproduction rate, Net reproduction rate.
Measurement of Mortality: Crude death rate, Standardized death rates, Agespecific death rates, Infant Mortality rate, the Death rate by cause.
Internal migration and its measurement, migration models, the concept of international migration.
Net migration. International and postcensal estimates. Projection method including logistic curve fitting. Decennial population census in India.
(iii) Survival Analysis and Clinical Trial:
Concept of time, order and random censoring, likelihood in the distributions – exponential, gamma, Weibull, lognormal, Pareto, Linear failure rate, inference for these distributions.
Life tables, failure rate, mean residual life, and their elementary classes and their properties. Estimation of survival function – actuarial estimator, Kaplan – Meier estimator, estimation under the assumption of IFR/DFR, tests of exponentiality against nonparametric classes, total time on the test.
Two sample problems – Gehan test, logrank test.
Semiparametric regression for failure rate – Cox’s proportional hazards model with one and several covariates, rank test for the regression coefficient.
Competing risk model, parametric and nonparametric inference for this model.
Introduction to clinical trials: the need and ethics of clinical trials, bias and random error in clinical studies, the conduct of clinical trials, an overview of Phase I – IV trials, multicenter trials.
Data management: data definitions, case report forms, database design, data collection systems for good clinical practice.
Design of clinical trials: parallel vs. crossover designs, crosssectional vs. longitudinal designs, review of factorial designs, objectives, and endpoints of clinical trials, design of Phase I trials, design of singlestage and multistage Phase II trials, design and monitoring of phase III trials with sequential stopping,
Reporting and analysis: analysis of categorical outcomes from Phase I – III trials, analysis of survival data from clinical trials.
(iv) Quality Control:
Statistical process and product control: Quality of a product, need for quality control, the basic concept of process control, process capability, and product control, general theory of control charts, causes of variation in quality, control limits, sub grouping summary of out of control criteria, charts for attributes p chart, np chart, cchart, V chart, charts for variables: R, (X, R), (X, σ) charts.
Basic concepts of process monitoring and control; process capability and process optimization.
General theory and review of control charts for attribute and variable data; O.C. and A.R.L. of control charts; control by gauging; moving average and exponentially weighted moving average charts; CuSum charts using Vmasks and decision intervals; Economic design of Xbar chart.
Acceptance sampling plans for attributes inspection; single and double sampling plans and their properties; plans for inspection by variables for the onesided and twosided specification.
(v) Multivariate Analysis:
Multivariate normal distribution and its properties. Random sampling from a multivariate normal distribution. Maximum likelihood estimators of parameters, distribution of the sample mean vector.
Wishart matrix – its distribution and properties, distribution of sample generalized variance, null and nonnull distribution of multiple correlation coefficients.
Hotelling’s T2 and its sampling distribution, application in test on mean vector for one and more multivariate normal population and also on equality of components of a mean vector in the multivariate normal population.
Classification problem: Standards of good classification, the procedure of classification based on multivariate normal distributions.
Principal components, dimension reduction, canonical variates, and canonical correlation — definition, use, estimation, and computation.
(vi) Design and Analysis of Experiments:
Analysis of variance for oneway and twoway classifications Need for the design of experiments, the basic principle of experimental design (randomization, replication, and local control), complete analysis and layout of the completely randomized design, randomized block design, and Latin square design, Missing plot technique. Split Plot Design and Strip Plot Design.
Factorial experiments and confounding in 2n and 3n experiments. Analysis of covariance. Analysis of nonorthogonal data. Analysis of missing data.
(vii) Computing with C and R:
Basics of C: Components of C language, the structure of a C program, Data type, basic data types, Enumerated data types, Derived data types, variable declaration, Local, Global, Parametric variables, Assignment of Variables, Numeric, Character, Real and String constants, Arithmetic, Relation and Logical operators, Assignment operators, Increment and decrement operators, conditional operators, Bitwise operators, Type modifiers and expressions, writing and interpreting expressions, using expressions in statements. Basic input/output.
Control statements: conditional statements, ifelse, nesting of ifelse, else if ladder, switch statements, loops in c, for, while dowhile loops, break, continue, exit ( ), goto, and label declarations, One dimensional two dimensional and multidimensional arrays. Storage classes: Automatic variables, External variables, Static variables, Scope, and a lifetime of declarations.
Functions: classification of functions, functions definition and declaration, assessing a function, return statement, parameter passing in functions. Pointers (concept only).
Structure: Definition and declaration; structure (initialization) comparison of structure variable; Array of structures: array within structures, structures within structures, passing structures to functions; Unions accessing a union member, the union of structure, initialization of a union variable, uses of the union. Introduction to the linked list, linearly linked list, insertion of a node in the list, removal of a node from the list.
Files in C: Defining and opening a file, inputoutput operation on a file, creating a file, reading a file. Statistics Methods and techniques in R.