Indian Statistical Service

1. General English 100 3 hrs.

2. General Studies 100 3 hrs.

3. Statistics-I (Objective) 200 2 hrs.

4. Statistics-II (Objective) 200 2 hrs.

5. Statistics-III (Descriptive) 200 3 hrs.

6. Statistics-IV (Descriptive) 200 3 hrs.

Note-1: Statistics I & II will be of Objective Type Questions (80 questions with maximum marks of
200 in each paper) to be attempted in 120 minutes.

Note-2: Statistics III and IV will be of Descriptive Type having Short Answer/ Small Problems
Questions (50%) and Long Answer and Comprehension problem questions (50%). At least one Short
Answer and One Long Answer Question from each section is compulsory.

In Statistics-IV, there will be SEVEN Sections in the paper. Candidates have to choose any TWO
Sections out of them. All Sections will carry equal marks.

Note-3: The papers on General English and General Studies, common to both Indian Economic
Service and Indian Statistical Service will be of subjective type.

Note-5: The details of standard and syllabi for the examination are given in Section-II below. 2. The
question papers in all subjects in Indian Economic Service Examination and in Indian Statistical
Service Examination will be of Conventional (essay) type except in Statistics Paper I and Statistics
Paper II which are Objective Type Papers.

PART - II Viva voce—

The candidate will be interviewed by a Board of competent and unbiased observers who will have
before them a record of his/her career. The object of the interview is to assess his/her suitability for
the service for which he/she has competed. The interview is intended to supplement the written
examination for testing the general and specialised knowledge and abilities for the candidate. The
candidate will be expected to have taken an intelligent interest not only in his/her subjects of
academic study but also in events which are happening around him/her both within and outside
his/her own State or Country as well as in modern currents of thought and in new discoveries which
should rouse the curiosity of well-educated youth.

The technique of the interview is not that of a strict cross-examination, but of a natural, through
directed and purposive conversation intended to reveal the candidate's mental qualities and his/her
grasp of problems. The Board will pay special attention to assess the intellectual curiosity, critical
powers of assimilation, balance of judgment and alertness of mind, the ability for social cohesion,
integrity of character initiative and capacity for leadership.

SECTION-II 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 theory by
facts, and to analyse 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 (COMM0N TO BOTH IES/ISS)

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.

GENERAL STUDIES (COMM0N TO BOTH IES/ISS)

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

STATISTICS-I (OBJECTIVE TYPE) (For ISS only)

(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, Hyper geometric, 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 0-1 law, Kolmogorov's 0-1 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.
Regression-linear, polynomial. Distribution of the correlation coefficient, Partial and multiple
correlation, Intraclass correlation, Correlation ratio. Standard errors and large sample test. Sampling
distributions of sample mean, sample variance, t, chi-square and F; tests of significance based on
them, small sample tests. Non-parametric tests-Goodness of fit, sign, median, run, Wilcoxon, Mann-
Whitney, WaldWolfowitz and Kolmogorov-Smirnov. Order statistics-minimum, 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, sub-division 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, concept of error
terms in interpolation formula. Inverse interpolation: Different methods of inverse interpolation.
Numerical differentiation: Trapezoidal, Simpson’s one-third and three-eight rule and Waddles 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 Runge-Kutta 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, 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 High level 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, 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.

ging and related concepts.

STATISTICS- II (OBJECTIVE TYPE) (For ISS only)

(i) Linear Models:

Theory of linear estimation, Gauss-Markov 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, generalized inverse of a matrix and
solution of normal equations, variances and covariances of least square estimators. One way and
two-way classifications, fixed, random and mixed effects models. Analysis of variance (two-way
classification only), multiple comparison tests due to Tukey, Scheffe and Student-Newmann-Keul-
Duncan.

(ii) Statistical Inference and Hypothesis Testing:

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. factorization theorem. Complete statistics. Rao-Blackwell
theorem. Confidence interval estimation. Optimum confidence bounds. Resampling, Bootstrap and
Jacknife. 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. Neyman-Pearson 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: Socio Economic Indicators, Gender Awareness/Statistics, Important Surveys and Censuses.

STATISTICS- III (DESCRIPTIVE TYPE) (For ISS only)

(i) Sampling Techniques:

Concept of population and sample, need for sampling, complete enumeration versus sampling, basic
concepts in sampling, sampling and Non-sampling 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 intra-class
correlation coefficient. Concept of multistage sampling and its application, two-stage sampling with
equal number of second stage units, estimation of population mean and total.Double sampling in
ratio and regression methods of estimation. Concept of Interpenetrating sub-sampling.

(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. Auto correlation, its consequences and
tests. Theil BLUS procedure, estimation and prediction, multi-collinearity 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, k-class 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 distribution-Pareto and Engel curves, Concentration curve, Methods of estimating
national income, Inter-sectoral 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. Time-series as discrete parameter
stochastic process, auto covariance 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. Detailed study of the stationary processes:
(1) moving average (MA), (2) auto regressive (AR), (3) ARMA and (4) AR integrated MA (ARIMA)
models. Box-Jenkins models, choice of AR and MA periods. Discussion (without proof) of estimation
of mean, auto covariance and autocorrelation functions under large sample theory, estimation of
ARIMA model parameters. Spectral analysis of weakly stationary process, periodogram and
correlogram analyses, computations based on Fourier transform.

STATISTICS-IV (DESCRIPTIVE TYPE) (For ISS only)

(Equal number of questions i.e., 50% weightage from all the subsections below and candidates have
to choose any two subsections and answer)

(i) Operations Research and Reliability:

Definition and Scope of Operations Research: phases in Operation Research, models and their
solutions, decision-making 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. Decision-making in the face
of competition, two-person games, pure and mixed strategies, existence of solution and 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 allowing quantity
discounts and shortages. Multi-item 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. Steady-state solutions of M/M/1 and M/M/c models with
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 sequence 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.

(ii) Demography and Vital Statistics:

Sources of demographic data, census, registration, ad-hoc surveys, Hospital records, Demographic
profiles of the Indian 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. 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 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 of
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 test 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 of clinical
trials, overview of Phase I – IV trials, multicenter trials. 19 Data management: data definitions, case
report forms, database design, data collection systems for good clinical practice. Design of clinical
trials: parallel vs. cross-over designs, cross-sectional vs. longitudinal designs, review of factorial
designs, objectives and endpoints of clinical trials, design of Phase I trials, design of single-stage and
multi-stage 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, 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, c-chart, 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; Cu-Sum
charts using V-masks and decision intervals; Economic design of X-bar chart. Acceptance sampling
plans for attributes inspection; single and double sampling plans and their properties; plans for
inspection by variables for one-sided and two sided specification.

(v) Multivariate Analysis:

Multivariate normal distribution and its properties. Random sampling from multivariate normal
distribution. Maximum likelihood estimators of parameters, distribution of sample mean vector.
Wishart matrix – its distribution and properties, distribution of sample generalized variance, null and
non-null 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 multivariate normal population. Classification problem:
Standards of good classification, 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 one way and two way classifications, Need for design of experiments, basic
principle of 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 and Strip Plot Design. Factorial experiments and confounding in 2n
and 3n experiments. Analysis of covariance. Analysis of non-orthogonal data. Analysis of missing
data.

(vii) 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, 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, if - else,
nesting of if - else, else if ladder, switch statements, loops in c, for, while, do - while 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 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, union of structure, initialization of a union
variable, uses of union. Introduction to linked list, linear linked list, insertion of a node in list, removal
of a node from list. 20 Files in C: Defining and opening a file, input – output operation on a file,
creating a file, reading a file. Statistics Methods and techniques in R.