# INDIAN STATISTICAL SERVICE EXAM SYLLABUS LATEST 2023 Exam

*INDIAN STATISTICAL SERVICE EXAM SYLLABUS LATEST 2023 exam *

**STATISTICS**

**Paper I**

**1. Probability:**

Â Â Elements of measure theory, Classical definitions and axiomatic approach. Sample space. Class of events and Probability measure. Laws of total and compound probability. Probability of m events out of n. Conditional probability, Bayesâ€™ theorem. Random variables - discrete and continuous. Distribution function. Standard probability distributions - Bernoulli, uniform, binomial, Poisson, geometric, rectangular, exponential, normal, Cauchy, hypergeometric, multinomial, Laplace, negative binomial, beta, gamma, lognormal and compound. Poisson distribution. Joint distributions, conditional distributions, Distributions of functions of random variables. Convergence in distribution, in probability, with probability one and in mean square.

Moments and cumulants. Mathematical expectation and conditional expectation. Characteristic function and moment and probability generating functions Inversion uniqueness and continuity theorems. Borel 0-1 law: Kolmogorovâ€™s 0-1 law. Tchebycheffâ€™s and Kolmogorovâ€™s inequalities.

Laws of large numbers and central limit theorems for independent variables. Conditional expectation and Martingales.

**2. Statistical Methods:**Â (a) 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. regression-linear, polynomial. Distribution of the correlation coefficient, Partial and multiple correlation, Intraclass correlation, Correlation ratio.(b) Standard errors and large sample test.

Sampling distributions of x,s2, t, chisqure and F; tests of significance based on them, Small sample tests. (c) Non-parametric tests-Goodness of fit, sign, median, run, Wicloxon, Mann-Whitney, Wald-Wolfowitz and Kolmogorov-Smirnov. Rank order statistics-minimum, maximum, range and median. Concept of Asymptotic relative effciency.

** 3. Numerical Analysis**

Interpolation formulae (with remainder terms) due to Lagrange, Newton-Gregory, Newton Divided different, Gauss and Striling. Euler-Maclaurinâ€™s summation formula.

**Inverse interpolation.**

Numerical integration and differentiation.

Difference equations of the first order.

Linear difference equations with constant coefficients.

**STATISTICS-II**

**1. Linear Models:Â **Â Theory of linear estimation. Gauss-Markoff setup. Least square estimators. Use of ginverse. analysis of one-way and two way classified data-fixed, mixed and random effect models. Tests for regression coefficients.

**2. Estimation:**Â Characteristics of good estimator. Estimation methods of maximum likelihood, minimum chi-square, moments and least squares. Optimal properties of maximum likelihood estimators. Minimum variance unbiased estimators. Minimum variance bound estimators. Cramer-Rao inequality. Bhattacharya bounds. Sufficient estimator. factorisation theorem. Complete statistics. Rao-Blackwell theorem. Confidence interval estimation. Optimum confidence bounds. Resampling, Bootstrap and Jacknife.

**3. Hypotheses testing and Statistical Quality Control:**Â (a) Hypothesis testing: Simple and composite hypothesis. Two kinds of error. Critical region. Different types of critical regions and similar regions. Power function. Mostpowerful and uniformly most powerful tests. Neyman-Pearson fundamental lemma. Unbiased test. Randomised test. Likelihood ratio test. Waldâ€™s SPRT, OC and ASN functions. Elements of decision and game theory. b) Statistical Quality Control: Control Charts for variable and attributes. Acceptance Sampling by attributes-Single, double, multiple and sequential Sampling plans; Concepts of AOQL and ATI; Acceptance Sampling by variables-use of Dodge-Romig and other tables.

**4. Multivariate Analysis:**Â Multivariate normal distribution. Estimation of mean Vector and covariance matrix. Distribution of Hotellingâ€™s T2-statistic, Mahalanobisâ€™s D2-statistic, and their use in testing. Partial and multiple correlation coefficients in samples from a multivariate normal population. Wishartâ€™s distribution, its reproductive and other properties. Wilkâ€™s criterion. Discriminant function. Principal components. Canonical variates and correlations.

**STATISTICS-III**

**1. Sampling Techniques:**Â Census versus sample survey. Pilot and large scale sample surveys. Role of NSS organisation. Simple random sampling with and without replacement. Stratified sampling and sample allocations. Cos and Variance functions. Ratio and Regression methods of estimation. Sampling with probability proportional to size. Cluster, double, multiphase, multistage and systematic sampling. Interpenetrating sub-sampling. Nonsampling errors.

**2. Design and Analysis of Experiments:Â **Principles of design of experiments. Layout and analysis of completely randomised, randomised block and Latin square designs. Factorial experiments and confounding in 2n and 3n experiments. Split-plot and strip-plot designs. Construction and analysis of balanced and partially balanced incomplete block designs. Analysis of covariance. Analysis of non-orthogonal data. analysis of missing and mixed plot data.

**3. Economic Statistics:**Â Components of time series. Methods of their determination-variate difference method. Yule-Slutsky effect. Correlogram. Autoregressive models of first and second order. Periodogram analysis.

Index numbers of prices and quantities and their relative merits. Construction of index numbers of wholesale and consumer prices. Income distribution- Pareto and Engel curves. Concentration curve. Methods of estimating national income. Inter-sectoral flows. Inter-industry table. Role of CSO.

**4. Econometrics:Â **Theory and analysis of consumer demand-specification and estimation of demand functions. Demand elasticities. Structure and model. Estimation of parameters in single equation model-classical least squares, generalised least-square, heteroscedasticity, serial correlation, multi-collinearity, errors in variable model. Simultaneous equation models-Identification, rank and other conditions. Indirect least squares and two stage least squares. Short-term economic forecasting.

**ISS Statistics - IV Syllabus**

Statistics - IV paper of Indian Statistical Services is of descriptive type with 80 questions and 200 marks. The duration of the paper is 3 hours. The syllabus hasÂ seven sections. You have to choose any two sections and answer. There are two questions in each section.

**1. Operations Research and Reliability**

Definition and Scope of Operations Research: phases in Operation Research, models and their solutions, decision makingÂ under uncertainty and risk, use of different criteria, sensitivity analysis.

Transportation and assignment problems. Bellman's principle of optimality, general formulation, computational methodsÂ and application of dynamic programming to LPP.

Decision-making in the face of competition, two-person games, pure and mixed strategies, existence of solution andÂ uniqueness of value in zero-sum games, finding solutions in 2x2, 2xm and mxn games.

Analytical structure of inventory problems, EOQ formula of Harris, its sensitivity analysis and extensions allowingÂ quantity discounts and shortages. Multi-item inventory subject to constraints. Models with random demand, the staticÂ risk model. P and Q- systems with constant and random lead times.

Queuing models - specification and effectiveness measures. Steady-state solutions of M/M/1 and M/M/c models withÂ associated distributions of queue-length and waiting time. M/G/1 queue and Pollazcek-Khinchine result.

Sequencing and scheduling problems. 2-machine n-job and 3-machine n-job problems with identical machine sequenceÂ for all jobs.

Branch and Bound method for solving travelling 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.

Life-distributions, 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 life-tests and in tests with replacement of failed items. Stress-strength reliability and its estimation.

**2. Demography and Vital Statistics**

Sources of demographic data, census, registration, ad-hoc surveys, Hospital records, Demographic profiles of the IndianÂ Census.

Complete life table and its main features, Uses of life table. Makehams and Gompertz curves. National life tables. UN model life tables. Abridged life tables. Stable and stationary populations.

Measurement of Fertility: Crude birth rate, General fertility rate, Age specific birth rate, Total fertility rate, Gross reproduction rate, Net reproduction rate.

Measurement of Mortality: Crude death rate, Standardized death rates, Age-specific death rates, Infant Mortality rate, Death rate by cause.

Internal migration and its measurement, migration models, concept of international migration. Net migration.Â International and postcensal estimates. Projection method including logistic curve fitting. Decennial population census in India.

**3. Survival Analysis and Clinical Trial**

Concept of time, order and random censoring, likelihood in the distributions - exponential, gamma, Weibull, lognormal,Â Pareto, Linear failure rate, inference for these distribution.

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 ofÂ IFR/DFR, tests of exponentiality against non-parametric classes, total time on test.

Two sample problem - Gehan test, log rank test.

Semi-parametric regression for failure rate - Cox's proportional hazards model with one and several covariates, rank testÂ for the regression coefficient.

Competing risk model, parametric and non-parametric inference for this model.

Introduction to clinical trials: the need and ethics of clinical trials, bias and random error in clinical studies, conduct ofÂ clinical trials, overview of Phase I - IV trials, multicenter trials.

Data management: data definitions, case report forms, database design, data collection systems for good clinicalÂ practice.

Design of clinical trials: parallel vs. cross-over designs, cross-sectional vs. longitudinal designs, review of factorialÂ designs, objectives and endpoints of clinical trials, design of Phase I trials, design of single-stage and multi-stage PhaseÂ II trials, design and monitoring of phase III trials with sequential stopping,Â Reporting and analysis: analysis of categorical outcomes from Phase I - III trials, analysis of survival data from clinicalÂ trials.

**4. Quality Control**

Statistical process and product control: Quality of a product, need for quality control, basic concept of process control,Â process capability and product control, general theory of control charts, causes of variation in quality, control limits, subÂ grouping summary of out of control criteria, charts for attributes p chart, np chart, c-chart, V chart, charts for variables:

R, (âˆ’X ,R), (âˆ’X ,Ïƒ) 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 byÂ gauging; moving average and exponentially weighted moving average charts; Cu-Sum charts using V-masks andÂ decision intervals; Economic design of X-bar chart.

Acceptance sampling plans for attributes inspection; single and double sampling plans and their properties; plans forÂ inspection by variables for one-sided and two sided specification.

**5. Multivariate Analysis**

Multivariate normal distribution and its properties. Random sampling from multivariate normal distribution. MaximumÂ likelihood estimators of parameters, distribution of sample mean vector.

Wishart matrix - its distribution and properties, distribution of sample generalized variance, null and non-nullÂ distribution of multiple correlation coefficients.

Hotelling's T2Â and its sampling distribution, application in test on mean vector for one and more multivariate normalÂ population and also on equality of components of a mean vector in multivariate normal population.

Classification problem: Standards of good classification, procedure of classification based on multivariate normalÂ distributions.

Principal components, dimension reduction, canonical variates and canonical correlation - definition, use, estimationÂ and computation.

**6. Design and Analysis of Experiments**

Analysis of variance for one way and two way classifications, Need for design of experiments, basic principle ofÂ experimental design (randomization, replication and local control), complete analysis and layout of completely randomized design, randomized block design and Latin square design, Missing plot technique. Split Plot Design andÂ Strip Plot Design.

Factorial experiments and confounding in 2nÂ and 3nÂ experiments. Analysis of covariance. Analysis of non-orthogonalÂ data. Analysis of missing data.

**7. Computing with C and R**

Basics of C: Components of C language, structure of a C program, Data type, basic data types, Enumerated data types,Â Derived data types, variable declaration, Local, Global, Parametric variables, Assignment of Variables, Numeric,Â Character, Real and String constants, Arithmetic, Relation and Logical operators, Assignment operators, Increment andÂ decrement operators, conditional operators, Bitwise operators, Type modifiers and expressions, writing and interpretingÂ expressions, using expressions in statements. Basic input/output.

Control statements: conditional statements, if - else, nesting of if - else, else if ladder, switch statements, loops in c, for,Â while, do - while loops, break, continue, exit ( ), goto and label declarations, One dimensional two dimensional andÂ multidimensional arrays. Storage classes: Automatic variables, External variables, Static variables, Scope and lifetime ofÂ declarations.

Functions: classification of functions, functions definition and declaration, assessing a function, return statement,Â parameter passing in functions. Pointers (concept only).

Structure: Definition and declaration; structure (initialization) comparison of structure variable; Array of structures:Â array within structures, structures within structures, passing structures to functions; Unions accessing a union member,Â union of structure, initialization of a union variable, uses of union. Introduction to linked list, linear linked list, insertionÂ of a node in list, removal of a node from list.

Files in C: Defining and opening a file, input - output operation on a file, creating a file, reading a file.Â Statistics Methods and techniques in R.

**ENGLISH**

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 degree examination of an Indian University in the relevant disciplines. The candidates will be expected to illustrate theory by facts, and to analyses 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 workman like use of words. Passages will usually be set for summary or precis.

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 degree examination of an Indian University in the relevant disciplines. The candidates will be expected to illustrate theory by facts, and to analyses 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 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 a nature which a candidate should be able to answer without special study.

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