Statistics

Jammu and Kashmir Public Services Commission (JKPSC)
Lecturer (10+2) Statistics
Subject / Paper: Statistics
Exam Cycle: 2025
Exam Type: Pen-and-Paper (OMR Based)
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COURSE OVERVIEW
Exam Name: Lecturer (10+2) Statistics
Conducting Authority: Jammu and Kashmir Public Services Commission (JKPSC)
Level: Competitive
Examination Type: MCQs
No. of Questions: 100 MCQs
Total Marks: 100 Marks
Duration: 2 Hours
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LIST OF UNITS (Verbatim)
Unit I: Statistical Methods
Unit II: Probability and Distribution Theory
Unit III: Statistical Inference
Unit IV: Sampling Theory
Unit V: Multivariate Analysis
Unit VI: Operations Research & Industrial Statistics
Unit VII: Linear Models and Regression Analysis
Unit VIII: Stochastic Process
Unit IX: Demography
Unit X: Design of Experiments
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UNIT-WISE DETAILED SYLLABUS (Verbatim)

Unit I: Statistical Methods

Topic 1: Descriptive Statistics, Measures of central tendency, arithmetic mean, geometric mean, harmonic mean, median and mode for grouped and ungrouped data with examples.
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Topic 2: Measures of dispersion, range, quartile deviation, variance, standard deviation, coefficient of variation, Skewness and Kurtosis.
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Topic 3: Basics of Correlation and regression, Scatter diagram, Karl Pearson’s coefficient of correlation, rank correlation, regression, lines of regression, regression coefficients, fitting of regression lines.
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Topic 4: Testing of hypothesis: Notion of hypothesis, null and alternative hypothesis, simple and composite hypothesis, test statistic, critical region, idea of one and two tailed test, type-I and type-II errors, level of significance, Hypothesis testing for mean and proportion.
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Topic 5: Uniformly most powerful (UMP) tests of unbiased tests.
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Topic 6: Likelihood ratio tests, Parameter Space, Properties of likelihood ratio test
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Topic 7: Chi- square test for independence of attributes.
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Topic 8: Non parametric tests, Advantages and disadvantages of non- parametric tests.
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Topic 9: Sign Test-one sample and two samples, Wilcoxon-Signed rank test,
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Topic 10: Linear rank statistics, distribution properties of the linear rank statistics.
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Unit II: Probability and Distribution Theory

Topic 1: Axiomatic approach to probability, Addition and multiplication theorem of probability, Conditional probability, Baye’s theorem.
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Topic 2: Random variables (discrete and continuous), Distribution function and its properties, Relation of distribution function with uniform variate.
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Topic 3: Univariate distributions, Bernoulli, Binomial, Poisson, Hyper-geometric, Geometric, Negative binomial, Discrete uniform, Power series, Continuous uniform, Normal, Exponential, Gamma, Beta, Cauchy, Weibull, Pareto, Laplace, Lognormal (elementary properties and applications only), Truncated distributions, Compound distributions.
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Topic 4: Functions of random variables, their distributions in case of univariate random variables and its applications.
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Topic 5: Sampling distributions t- distribution, F-distribution,
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Unit III: Statistical Inference

Topic 1: Concept of statistical inference, Criteria of good estimators, unbiasedness, consistency, efficiency and sufficiency.
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Topic 2: principle, factorization theorem, minimal sufficiency,
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○ minimal sufficient partition, construction of minimal sufficient statistic, minimal sufficient statistic for exponential families, power series family and pitman family.
Topic 3: Completeness, bounded completeness, ancillary statistic.
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Topic 4: Point estimation, unbiased estimators, minimum variance unbiased estimator (MVUE).
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Topic 5: Rao-Blackwell and Lehmann-Scheffe theorems and their uses.
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Topic 6: Necessary and sufficient condition for MVUE.
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Topic 7: Methods of Estimation, Method of maximum likelihood estimation (MLE) and small sample properties of MLE.
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Topic 8: Method of moments, Method of minimum chi-square, Method of scoring.
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Topic 9: Testing of hypothesis, Basic concepts, randomized and nonrandomized test procedures,
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Topic 10: Neyman-Pearson Lemma, Families with MLR property, UMP Test with applications to exponential families, UMP unbiased tests with application to one sample and two sample problems in normal populations.
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Topic 11: Likelihood ration test and its properties (without proof) and applications to normal distribution,
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Topic 12: Interval estimation, confidence level, construction of confidence, intervals using pivots, shortest expected length confidence interval,
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Topic 13: Wald’s SPRT
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Unit IV: Sampling Theory

Topic 1: Concepts of population and sample, need for sampling, census and sample surveys,
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Topic 2: designing of a questionnaire, sampling and non-sampling errors, sample size determination,
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Topic 3: finite population sampling techniques-SRSWR, SRSWOR, estimation of mean and total in each case and their variances.
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Topic 4: Stratified sampling, allocation problems in stratified sampling, estimation of mean or total in each case and their variances.
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Topic 5: Systematic sampling: Linear and circular systematic sampling. The sample mean and its variance, comparison of systematic sampling with random sampling, comparison of systematic sampling with stratified sampling.
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Topic 6: Unequal probability sampling, PPSWR Methods, cumulative total method, Lahiri’s method, related estimation problems, PPSWOR method and related estimation of a finite population mean.
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Topic 7: Ratio and regression estimators based on SRSWOR method of sampling,
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Topic 8: Double sampling, Cluster sampling, Two-stage sampling with equal number of second stage units.
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Unit V: Multivariate Analysis

Topic 1: Multivariate normal distribution and its properties,
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Topic 2: Maximum likelihood estimates of mean vector and dispersion matrix,
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Topic 3: Distribution of sample mean vector, Wishart matrix-its distribution and properties.
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Topic 4: Null distribution of simple, partial and multiple correlation coefficients and their testing of significance.
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Topic 5: Hotelling’s T2T2 statistic-its distribution and application in testing of mean vector for one and more multivariate normal populations,
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Topic 6: Mahalanobis D2D2 statistic and its applications.
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Topic 7: Problem of classification, probabilities of misclassification and their estimation, classification into more than two multivariate normal populations,
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Topic 8: Discrimination procedures for discriminating between two multivariate populations-sample discriminant function.
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Topic 9: Principal Components Analysis, Factor Analysis, Canonical variates and canonical correlations,
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Topic 10: Multivariate Analysis of Variance (MANOVA) of one- and two-way classified data.
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Unit VI: Operations Research & Industrial Statistics

Topic 1: Scope of Operational research, Necessity of Operations Research in Industry; phases in Operations Research.
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Topic 2: Linear Programming, Simplex method and Extreme point theorems, Revised Simplex Method,
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Topic 3: Transportation and Assignment Problems with their methods of solution.
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Topic 4: Duality in LPP, Symmetric and asymmetric dual problems, duality theorems, Primal-Dual Relations, Complementary Slackness Theorem and Complementary Slackness conditions, Dual Simplex Method.
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Topic 5: Statistical Quality Control, Stewarts control chart, Statistical basis of a control chart, control chart for variables (X, R, & S) charts.
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Topic 6: Control charts for attributes (np, p & C) charts.
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Topic 7: Moving average charts.
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Topic 8: Operating Characteristic function (OC) and Average Run length (ARL) of X-bar chart.
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Topic 9: Capability indices Cp, Cpk and Cpm. estimation, confidence intervals relating to capability indices for normally distributed characteristics.
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Topic 10: Reliability concepts, hazard rate, distribution of longevity and moments.
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Topic 11: Some important theorems based on reliability theory.
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Unit VII: Linear Models and Regression Analysis

Topic 1: Linear models, Gauss Markov set up, Model classification,
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Topic 2: Normal equations and least squares estimates, Error and estimation space,
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Topic 3: Variance and covariance of least square estimates,
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Topic 4: Estimation of error variance, estimation with correlated observations, least square estimates with restriction on parameters.
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Topic 5: Experimental Design Models, Introduction, Point estimation, Re-parameterization, Variance and Covariance of estimable function, testing of hypotheses, Regression models.
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Topic 6: Simple linear regression fit of polynomials,
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Topic 7: Residual and their plot as tests for departure from assumption such as fitness of model, normality, and homogeneity of variances and detection of outliers,
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Topic 8: Analysis of covariance, estimation and testing ,one way model with one covariance, two way model with two covariance
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Topic 9: Simple linear regression model, Assumptions and estimation of model parameters,
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Topic 10: Standard error of estimators,
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Topic 11: Testing of hypotheses on slope and intercept.
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Topic 12: Coefficient of determination (R2).
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Unit VIII: Stochastic Process

Topic 1: Definition of Stochastic process, Finite dimensional distributions.
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Topic 2: Examples of various stochastic processes.
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Topic 3: Markov chain and its Examples.
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Topic 4: Chapman-Kolmogorov equation, calculation of n-step transition probabilities.
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Topic 5: Classification of states of Markov chain, irreducible Markov chain, period of the state, First entrance theorem, First passage time distribution.
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Topic 6: Long run distribution of Markov chain, relation of mean recurrence time and stationary distribution.
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Topic 7: Random walk and gambler’s ruin problem.
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Topic 8: Discrete state space continuous time Markov chain.
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Topic 9: Poisson process and related results.
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Topic 10: Birth and death processes and associated cases.
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Topic 11: M/M/1, M/M/S queuing models and related properties,
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Topic 12: Galton-Watson branching process.
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Topic 13: Probability of ultimate extinction, distribution of population size and associated results.
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Topic 14: Simulation of Markov chain, Poisson process, branching process (Algorithms).
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Unit IX: Demography

Topic 1: Introduction to Demography, Definition and uses of demographic data,
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Topic 2: Source of vital statistics: Census method-Registration method,
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Topic 3: Sources of demography data: secondary sources – SRS- surveys.
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Topic 4: Mortality and Fertility, Nature and uses of mortality statistics,
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Topic 5: Mortality measures: Crude death rate (CDR) and Age-specific death rates (ASDR), Infant mortality rate (IMR).
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Topic 6: Fertility measures, Basic terms and concepts used in the study of fertility,
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Topic 7: Measures of fertility: Crude birth rate(CBR), Age specific fertility rate (ASFR), General fertility rate (GFR), Total fertility rate (TFR).
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Topic 8: Measurement of Population Growth, Pearl’s vital index, Gross reproductive rate (GRR) and Net reproductive rate (NRR).
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Topic 9: Life table: Description of life table, construction of complete and abridged life tables, uses of life table.
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Topic 10: Concept of mobility and migration, types of migration, internal migration and its measurement, migration models, concept of international migration.
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Topic 11: Net-migration.
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Topic 12: International and postcensal estimates.
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Topic 13: Projection method including logistic curve fitting.
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Topic 14: Decennial population census in India.
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Unit X: Design of Experiments

Topic 1: Fixed, random and mixed effects linear models,
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Topic 2: Introduction to Design of Experiments: General Block Design and its information matrix (C), Criteria for connectedness, balance and orthogonality, intrablock analysis.
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Topic 3: CRD, RBD and LSD,
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Topic 4: Missing plot techniques in RBD and LSD,
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Topic 5: Symmetrical Factorial experiments with factors at two and three levels (2n2n, 3232, 3333),
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Topic 6: Confounding-Total and Partial in factorial experiments,
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Topic 7: Split plot Design, Strip plot design.
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Topic 8: Balanced incomplete block designs, partially balanced incomplete block design, methods of constructions and their analysis and Lattice.
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Topic 9: Analysis of Covariance in RBD, LSD and CRD,
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Topic 10: Analysis of Covariance in Non-orthogonal Data in two-way classification,
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Topic 11: Covariance and Analysis of experiments with missing observation.
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EXAM STRUCTURE / SCHEME OF EXAMINATION
• Not explicitly provided in the uploaded document.
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SYLLABUS SUMMARY (Auto-Generated)
• Total Units: 10
• Total Topics: 113
• Exam: Lecturer (10+2) Statistics
• Subject: Statistics
• Exam Year: 2025
✓ Extracted verbatim from the official uploaded document