**INDIAN STATISTICAL SERVICE EXAMINATION, 2016**

** ****Age Limit:** A candidate must have attained the age of 21 years and must not have attained the age of 30 years on 1st August, 2016.

** ****Minimum Educational Qualifications:**

A candidate for the Indian Statistical Service must have obtained a Bachelor’s Degree with Statistics/Mathematical Statistics/Applied Statistics as one of the subject or a Master’s degree in Statistics/Mathematical Statistics/Applied Statistics.

**Indian Statistical Service**

Si.No | Subject | Maximum Marks | Time |

1 | General English | 100 | 3 hrs |

2 | General Studies | 100 | 3hrs |

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

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

5 | Statistics-III (Subjective) | 200 | 3hrs |

6 | Statistics-IV (Subjective) | 200 | 3hrs |

**Mains syllabus**

## ISS Statistics I Syllabus

**Probability**

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, Bayes’ theorem. Random variables – discrete and continuous. Distribution function. Standard probability distributions – Bernoulli, uniform, binomial, Poisson, geometric, rectangular, exponential, normal, Cauchy, hyper geometric, 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: Kolmogorov’s 0-1 law. Tchebycheff’s and Kolmogorov’s inequalities. Laws of large numbers and central limit theorems for independent variables. Conditional expectation and Martingales.

**Statistical Methods**

(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 efficiency.

**Numerical Analysis**

Interpolation formulae (with remainder terms) due to Lagrange, Newton-Gregory, Newton Divided different, Gauss and Striling. Euler-Maclaurin’s summation formula. Inverse interpolation. Numerical integration and differentiation. Difference equations of the first order. Linear difference equations with constant coefficients.

** ISS Statistics II Syllabus**

**Linear Models**

Theory of linear estimation. Gauss-Markoff setup. Least square estimators. Use of g-inverse. analysis of one-way and two way classified data-fixed, mixed and random effect models. Tests for regression coefficients.

**Estimation**

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.

**Hypotheses testing and Statistical Quality Control**

(a) Hypothesis testing: Simple and composite hypothesis. 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. Randomised test. Likelihood ratio test. Wald’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.
**Multivariate Analysis**

Multivariate normal distribution. Estimation of mean Vector and covariance matrix. Distribution of Hotelling’s T2-statistic, Mahalanobis’s D2-statistic, and their use in testing. Partial and multiple correlation coefficients in samples from a multivariate normal population. Wishart’s distribution, its reproductive and other properties. Wilk’s criterion. Discriminant function. Principal components. Canonical variates and correlations.

## ISS Statistics III Syllabus

**Sampling Techniques**

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. Non-sampling errors.

**Design and Analysis of Experiments**

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.

**Economic Statistics**

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.

**Econometrics**

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

**Stochastic Processes**

Specifications of a Stochastic Process, Markov chains, classification of states, limiting probabilities; stationary distribution; Random walk and Gambler’s ruin problem. Poisson process, Birth and death process; applications to Queues-M/M/I and M/M/C models. Branching Process.

**Operations Research**

Elements of linear programming. Simplex procedure. Principle of duality. Transport and assignment problems. Single and multi-period inventory control models. ABC analysis. General simulation problems. Replacement models for items that fail and or items that deteriorate.

**Demography and Vital Statistics**

The life table, its constitution and properties. Makehams and Gompertz curves. National life tables. UN model life tables. Abridged life tables. Stable and stationary populations. Different birth rates. Total fertility rate. Gross and net reproduction rates. Different mortality rates. Standardised death rate. Internal and international migration: net migration. International and postnasal estimates. Projection method including logistic curve fitting. Decennial population census in India.

**Computer Application and Data Processing**

**(a) Computer Application**

**Computer system concepts:** Computer system components and functions. The Central Processing unit, Main memory, Bit, Byte, Word, Input/Output Devices, Speeds and memory Capacities in computer systems.

**Software concepts:** Overview of Operating Systems, Types and Functions of Operating System, application Software, Software for multi-tasking, multi-programming, Batch Processing Mode, Time sharing mode, Concept of System Support Programme, Overview of Existing Software packages on Word Processing and Spread sheets.

**Overview of an application Specific Programme:** Flow charts, Basics of Algorithm, Fundamental of design and analysis of Algorithm; Basics of data structure, Queue, Stack.

**(b) Data Processing**

**Data processing:** Digital Number System, Number conversions, Binary representation of integers, Binary representation of real numbers, Logical Data element like character, fields, records, files, Fundamentals of data transmission and processing including error control and error processing.

**Data base management:** Data Resource management. Data base and file organisation and processing. (a) Direct, (b) Sequential, (c) Indexed Sequential file. Concepts of Client Server architecture, Data Base Administrator. An overview of DBMS software.