# UPSC Statistics Syllabus

Statistics is a popular choice for UPSC IAS optional subject among the candidates having background in the relevant field. Preparation for this subject requires in-depth knowledge of its syllabus. It is through the syllabus that the candidates gain familiarity with the important topics from which the questions might be asked in the exam. To provide the aspirants this familiarity, this article presents the complete details of the UPSC Statistics Syllabus 2023. There will be two papers in the UPSC Civil Services Statistics exam for which the syllabi can be found here.

## Statistics Syllabus for UPSC Civil Services

To obtain good score in any exam, it is important to study according to the syllabus. Especially when you are preparing for the civil services, it becomes even more important. So carefully check the UPSC Statistics syllabus 2023 from the post below and make sure that you do not leave any of the given topics.

### Syllabus of Paper I

1. Probability:

Chebyshev’s Inequality and Khintchine’s Weak Law of Large Numbers, Strong Law of Large Numbers and Kolmogorov’s Theorems, Sample Space and Events, Probability Measure and Probability Space, Random Variable As A Measurable Function, Stochastic Independence of Events and of Random Variables, Expectation and Moments of A Random Variable, Distribution Function of A Random Variable, Discrete and Continuous-Type Random Variable, Probability Mass Function, Probability Density Function, Vector-Valued Random Variable, Marginal and Conditional Distributions, Conditional Expectation, Convergence of A Sequence of Random Variable In Distribution, In Probability, In Path Mean and Almost Everywhere, Their Criteria and Inter-Relations, Inversion Theorem, Lindeberg and Levy Forms of Central Limit Theorem, Standard Discrete and Continuous Probability Distributions, Probability Generating Function, Moment Generating Function, Characteristic Function

1. Statistical Inference:

Bayes Estimators, Non-Randomized and Randomized Tests, Critical Function, MP Tests, Neyman-Pearson Lemma, UMP Tests, Monotone Likelihood Ratio: Similar and Unbiased Tests, Consistency, Unbiasedness, Efficiency, Sufficiency, Completeness, Ancillary Statistics, Minimum Chi Square and Modified Minimum Chi Square, Properties of Maximum Likelihood and Other Estimators, Asymptotic Efficiency, Factorization Theorem, Exponential Family of Distribution and Its Properties, Uniformly Minimum Variance Unbiased (UMVU) Estimation, Rao-Blackwell and Lehmann-Scheffe Theorems, Wilcoxon Signed-Rank Test and Its Consistency, Kolmogorov-Smirnov Two Sample Test, Run Test, Wilcoxon-Mann-Whitney Test and Median Test, Their Consistency and Asymptotic Normality, Wald’s SPRT and Its Properties, OC and ASN Functions For Tests Regarding Parameters For Bernoulli, Poisson, Normal and Exponential Distributions. Wald’s Fundamental Identity, Cramer-Rao Inequality for Single Parameter, Estimation By Methods of Moments, Maximum Likelihood, Least Squares, Prior and Posterior Distributions, Loss Function, Risk Function, Minimax Estimator, UMPU Tests For Single Parameter Likelihood Ratio Test and Its Asymptotic Distribution. Confidence Bounds and Its Relation with Tests, Kolmogorov’s Test for Goodness of Fit and Its Consistency, Sign Test and Its Optimality

1. Linear Inference and Multivariate Analysis:

Estimation of Variance and Covariance Components, Multivariate Normal Distribution, Mahalanobis’ D2 and Hotelling’s T2 Statistics and Their Applications and Properties, Discriminant Analysis, Canonical Correlations, Principal Component Analysis, Linear Statistical Models, Theory of Least Squares and Analysis of Variance, Regression Analysis, Linear Regression, Curvilinear Regression and Orthogonal Polynomials, Multiple Regression, Multiple and Partial Correlations, Gauss-Markov Theory, Normal Equations, Least Squares Estimates and Their Precision, Test of Significance and Interval Estimates Based On Least Squares Theory In One-Way, Two-Way and Three-Way Classified Data

1. Sampling Theory and Design of Experiments:

Simple Random Sampling With and Without Replacement, Stratified Random Sampling, Systematic Sampling and Its Efficacy, Cluster Sampling, Two Stage and Multi-Stage Sampling, An Outline of Fixed-Population and Super-Population Approaches, Non-Sampling Errors, Fixed Effects Model (Two-Way Classification), Random and Mixed Effects Models (Two-Way Classification With Equal Observation Per Cell), CRD, RBD, LSD and Their Analyses, Distinctive Features of Finite Population Sampling, Probability Sampling Designs, Ratio and Regression Methods of Estimation Involving One Or More Auxiliary Variables, Split-Plot and Simple Lattice Designs, Transformation of Data Duncan’s Multiple Range Test, Two-Phase Sampling, Probability Proportional To Size Sampling With and Without Replacement, The Hansen-Hurwitz and The Horvitz-Thompson Estimators, Non-Negative Variance Estimation With Reference To The Horvitz-Thompson Estimator, Incomplete Block Designs, Concepts of Orthogonality and Balance, BIBD, Missing Plot Technique, Factorial Experiments and 24 and 32, Confounding In Factorial Experiments

### Syllabus of Paper II

1. Industrial Statistics

Concept of Reliability, Failure Rate and Reliability Functions, Reliability of Series and Parallel Systems and Other Simple Configurations, Process and Product Control, General Theory of Control Charts, Different Types of Control Charts For Variables and Attributes, X, R, S, P, NP and Charts, Cumulative Sum Chart, Single, Double, Multiple and Sequential Sampling Plans For Attributes, OC, ASN, AOQ and ATI Curves, Concepts of Producer’s and Consumer’s Risks, AQL, LTPD and AOQL, Sampling Plans For Variables, Use of Dodge-Romig Tables, Renewal Density and Renewal Function, Failure Models: Exponential, Weibull Normal, Lognormal, Problems In Life Testing, Censored and Truncated Experiments For Exponential Models

1. Optimization Techniques:

Rectangular Games, Two-Person Zero Sum Games, Methods of Solution (Graphical and Algebraic), Replacement of Failing Or Deteriorating Items, Group and Individual Replacement Policies, Different Types of Models In Operations Research, Their Construction and General Methods of Solution, Simulation and Monte-Carlo Methods Formulation of Linear Programming (LP) Problem, Simple LP Model and Its Graphical Solution, Storage Models With Particular Reference To Dam Type, Homogeneous Discrete-Time Markov Chains, Transition Probability Matrix, The Simplex Procedure, The Two-Phase Method and The M-Technique With Artificial Variables, The Duality Theory of LP and Its Economic Interpretation, Sensitivity Analysis, Transportation and Assignment Problems, Concept of Scientific Inventory Management and Analytical Structure of Inventory Problems, Simple Models With Deterministic and Stochastic Demand With and Without Lead Time, Classification of States and Ergodic Theorems, Homogeneous Continuous-Time Markov Chains, Poisson Process, Elements of Queuing Theory, M/MI, M/M/K, G/M/L and M/G/1 Queues, Solution of Statistical Problems On Computers Using Well Known Statistical Software Packages Like SPSS

1. Quantitative Economics and Official Statistics:

General Linear Model, Ordinary Least Square and Generalized Least Squares Methods of Estimation, Problem of Multi-Collinearity, Consequences and Solutions of Multi-Collinearity, Autocorrelation and Its Consequences, Heteroscedasticity of Disturbances and Its Testing, Test For Independence of Disturbances, Determination of Trend, Seasonal and Cyclical Components, Box-Jenkins Method, Tests For Stationary Series, ARIMA Models and Determination of Orders of Autoregressive and Moving Average Components, Fore-Casting, Commonly Used Index Numbers- Laspeyres’, Paasche’s and Fisher’s Ideal Index Numbers, Cham-Base Index Number, Uses and Limitations of Index Numbers, Index Number of Present Official Statistical System In India Relating To Population, Agriculture, Industrial Production, Trade and Prices, Methods of Collection of Official Statistics, Their Reliability and Limitations, Principal Publications Containing Such Statistics, Various Official Agencies Responsible For Data Collection and Their Main Functions, Wholesale Prices, Consumer Price, Agricultural Production and Industrial Production, Test For Index Numbers- Proportionality, Time-Reversal, Factor-Reversal and Circular, Concept of Structure and Model For Simultaneous Equations, Problem of Identification-Rank and Order Conditions of Identifiability, Two-Stage Least Square Method of Estimation

1. Demography and Psychometry:

Population Projection, Stable Population, Quasi-Stable Population, Techniques In Estimation of Demographic Parameters, Standard Classification By Cause of Death, Health Surveys and Use of Hospital Statistics, Demographic Data From Census, Registration, NSS Other Surveys, Their Limitations and Uses, Definition, Construction and Uses of Vital Rates and Ratios, Measures of Fertility, Methods of Standardization of Scales and Tests, Z-Scores, Standard Scores, T-Scores, Percentile Scores, Intelligence Quotient and Its Measurement and Uses, Validity and Reliability of Test Scores and Its Determination, Use of Factor Analysis and Path Analysis In Psychometry, Reproduction Rates, Morbidity Rate, Standardized Death Rate, Complete and Abridged Life Tables, Construction of Life Tables From Vital Statistics and Census Returns, Uses of Life Tables, Logistic and Other Population Growth Curves, Fitting A Logistic Curve

Statistics