BPSC Statistics Syllabus 2026: Section-wise Optional Syllabus Topics & PDF

The BPSC Statistics Syllabus 2026 outlines all the topics prescribed for the Statistics optional subject in the Bihar Public Service Commission examination. It is divided into Section I and Section II, covering both theoretical concepts and applied statistical methods. The syllabus includes Probability, Statistical Inference, Linear Inference, Sampling Theory, Operational Research, Engineering Statistics, Quantitative Economics, Demography, and Psychometry.

A clear understanding of the BPSC Syllabus helps you plan your preparation, identify important topics, and allocate sufficient time to each section. Since the optional paper combines mathematical concepts with practical statistical applications, covering every topic mentioned in the official syllabus is essential.

BPSC Statistics Syllabus Overview

The BPSC Statistics optional syllabus consists of two sections. Candidates should prepare every topic thoroughly, as the examination allows candidates to answer a maximum of three questions from each section. 

BPSC Statistics Syllabus for Section I

Section I focuses on the theoretical foundations of statistics. It covers probability theory, estimation, hypothesis testing, regression analysis, and multivariate statistical techniques. 

Probability

This unit introduces the fundamental concepts of probability. Important topics include: 

• Sample space and events

• Probability measures and probability space

• Statistical independence

• Random variables

• Discrete and continuous probability distributions

• Probability density and distribution functions

• Marginal and conditional distributions

• Expectation and moments

• Conditional expectation

• Correlation coefficient

• Convergence in probability

• Convergence in LP and almost everywhere

• Markov, Chebyshev, and Kolmogorov inequalities

• Borel-Cantelli Lemma

• Weak and Strong Law of Large Numbers

• Probability generating functions

• Characteristic functions

• Uniqueness and continuity theorems

• Distribution determined by moments

• Lindeberg-Levy Central Limit Theorem

• Standard discrete and continuous probability distributions and their limiting cases

Statistical Inference

This section explains methods used for parameter estimation and hypothesis testing.

Topics include:

• Properties of estimators

• Consistency

• Unbiasedness

• Efficiency

• Sufficiency

• Completeness

• Cramer-Rao Bound

• Minimum Variance Unbiased Estimation

• Rao-Blackwell Theorem

• Lehmann-Scheffe Theorem

• Method of Moments

• Maximum Likelihood Estimation

• Minimum Chi-square Estimation

• Confidence intervals

• Simple and composite hypotheses

• Statistical tests

• Critical regions

• Type I and Type II errors

• Power function

• Most Powerful and Uniformly Most Powerful Tests

• Neyman-Pearson Lemma

• Likelihood Ratio Test

• Sign Test

• Wilcoxon-Mann-Whitney Test

• Kolmogorov-Smirnov Test

• Distribution-free confidence intervals

• Chi-square goodness of fit test

• Run Test

• Sequential Probability Ratio Test (SPRT)

Linear Inference and Multivariate Analysis

This unit covers regression analysis, analysis of variance, and multivariate statistical techniques.

Topics include:

• Theory of Least Squares

• Analysis of Variance (ANOVA)

• Gauss-Markov Theory

• Normal Equations

• Precision of Least Square Estimates

• Tests of significance

• Confidence intervals

• One-way, Two-way, and Three-way classification

• Linear Regression

• Regression Coefficients

• Correlation Analysis

• Curvilinear Regression

• Orthogonal Polynomials

• Test for Linearity

• Multivariate Normal Distribution

• Multiple Regression

• Multiple Correlation

• Partial Correlation

• Mahalanobis D² Statistic

• Hotelling T² Statistic

• Fisher's Discriminant Analysis

BPSC Statistics Syllabus for Section II

Section II focuses on the practical application of statistical methods in surveys, industries, economics, operations research, and population studies. 

Sampling Theory and Design of Experiments

Important topics include: 

• Nature and scope of sampling

• Simple Random Sampling

• Sampling with and without replacement

• Standard error estimation

• Probability Proportional to Size (PPS) Sampling

• Stratified Sampling

• Systematic Sampling

• Cluster Sampling

• Two-stage and Multi-stage Sampling

• Multiphase Sampling

• Estimation of population mean and total

• Auxiliary variables

• Ratio and Regression Estimation

• Double Sampling

• Cost and variance functions

• Planning and organisation of sample surveys

• Large-scale sample surveys conducted in India

• Principles of Experimental Design

• Completely Randomised Design (CRD)

• Randomised Block Design (RBD)

• Latin Square Design (LSD)

• Missing Plot Technique

• Factorial Designs

• Confounding

• Fractional Replication

• Split Plot Design

• Balanced Incomplete Block Design (BIB)

• Simple Lattice Design

Engineering Statistics

Topics include:

• Quality control concepts

• Control Charts

• X̄-R Charts

• P Charts

• np Charts

• Cumulative Sum Charts

• Sampling Inspection

• Acceptance Sampling

• Single, Double, Multiple, and Sequential Sampling Plans

• Producer's Risk

• Consumer's Risk

• AQL

• LTPD

• Reliability

• Maintainability

• Availability

• Failure Rate

• Bathtub Curve

• Exponential Distribution

• Weibull Distribution

• Reliability of Series and Parallel Systems

• Redundancy Techniques

• Life Testing

Operational Research

Important topics are:

• Operations Research models

• Discrete and Continuous Time Markov Chains

• Transition Probability Matrix

• Classification of States

• Queuing Theory

• M/M/1 and M/M/K Models

• Inventory Management

• Storage Models

• Linear Programming

• Simplex Method

• Two-Phase Method

• Big M Method

• Duality Theory

• Sensitivity Analysis

• Transportation Problem

• Assignment Problem

• Replacement Models

• Introduction to Fortran IV Programming

• Statistical applications using programming

Quantitative Economics

Topics include: 

• Time Series Analysis

• Additive and Multiplicative Models

• Trend Analysis

• Moving Average Method

• Seasonal Indices

• Index Numbers

• Laspeyres Index

• Paasche Index

• Edgeworth-Marshall Index

• Fisher Index

• Cost of Living Index

• Demand Functions

• Demand Elasticity

• Production Theory

• Supply Functions

• Least Squares Estimation

• Generalised Least Squares

• Heteroscedasticity

• Serial Correlation

• Multicollinearity

• Simultaneous Equation Models

• Two-Stage Least Squares

• Economic Forecasting

Demography and Psychometry

Topics include: 

• Sources of demographic data

• Census

• Civil Registration

• National Sample Survey

• Vital Statistics

• Fertility Measures

• Mortality Measures

• Life Tables

• Population Growth Models

• Gross and Net Reproduction Rate

• Stable Population Theory

• Morbidity Statistics

• Health Surveys

• Hospital Statistics

• Educational Statistics

• Psychological Testing

• Standardisation of Tests

• Intelligence Quotient (IQ)

• Reliability of Tests

• T Scores

• Z Scores

BPSC Statistics Syllabus PDF

The official BPSC Statistics Syllabus PDF is available in the notification issued by the Bihar Public Service Commission. Downloading the official syllabus helps you understand the complete topic list, paper structure, and subject-wise coverage.

Before starting your preparation, compare your study material with the official syllabus and prepare a checklist to track your progress. Referring to the official PDF throughout your preparation ensures that no topic is overlooked. 

Download BPSC Statistics Syllabus PDF

The BPSC Statistics Syllabus covers both theoretical and applied areas of statistics, making it one of the more comprehensive optional subjects in the examination. A structured preparation strategy, regular revision, and thorough coverage of every topic prescribed in the official syllabus can help build a strong foundation for the Statistics optional paper. Always refer to the latest syllabus released by the Bihar Public Service Commission before beginning your preparation.