Paper I of the Indian Statistical Service written examination is Statistics-I, and this page takes its syllabus one line at a time. Each line is reproduced as it is prescribed, then pointed at the page on this site that teaches it, with the depth stated rather than implied.
Statistics-I (Objective) — 200 marks, 2 hrs.
Examination Notice No. 07/2026-IES/ISS, dated 11.02.2026 — Appendix-I, Scheme of Examination, and Section-II, Standard and Syllabi11 syllabus lines: 11 taught in depth, 0 at exam level, 0 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Classical and axiomatic definitions of probability and consequences; law of total probability, conditional probability, Bayes' theorem and applications | Theory of Probability Unit 1 — Elementary Probability | deep |
| Discrete and continuous random variables; distribution functions and their properties | Theory of Probability Unit 2 — Univariate Random Variables | deep |
| Standard discrete and continuous distributions — Bernoulli, uniform, binomial, Poisson, geometric, rectangular, exponential, normal, Cauchy, hypergeometric, multinomial, Laplace, negative binomial, beta, gamma, lognormal | Theoretical Discrete Distributions Theoretical Continuous Distributions | deep |
| The same families with their generating functions, and the relations between them derived rather than tabulated | Distribution Theory Unit 1 — Lognormal, Weibull, Pareto, Laplace and Cauchy | deep |
| Random vectors, joint and marginal distributions, conditional distributions, distributions of functions of random variables | Theory of Probability Unit 3 — Bivariate Random Variables | deep |
| Modes of convergence of sequences of random variables — in distribution, in probability, with probability one and in mean square | Probability Theory Unit 3 — Convergence of Sequences of Random Variables | deep |
| Mathematical expectation and conditional expectation | Probability Theory Unit 2 — Expectation, Characteristic Functions and Inequalities | deep |
| Characteristic function, moment and probability generating functions; inversion, uniqueness and continuity theorems | Probability Theory Unit 2 — Expectation, Characteristic Functions and Inequalities Probability Theory Unit 4 — Laws of Large Numbers and Central Limit Theorems | deep |
| Borel 0–1 law, Kolmogorov's 0–1 law; Tchebycheff's and Kolmogorov's inequalities | Probability Theory Unit 3 — Convergence of Sequences of Random Variables Probability Theory Unit 2 — Expectation, Characteristic Functions and Inequalities | deep |
| Laws of large numbers and central limit theorems for independent variables | Probability Theory Unit 4 — Laws of Large Numbers and Central Limit Theorems | deep |
| Order statistics — minimum, maximum, range and median | Distribution Theory Unit 4 — Quadratic Forms and Order Statistics | deep |
12 syllabus lines: 11 taught in depth, 0 at exam level, 1 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Collection, compilation and presentation of data; charts, diagrams and histogram; frequency distribution | Descriptive Statistics Unit 1 — Statistical Description of Data Descriptive Statistics Unit 2 — Measurement Scales & Data Presentation | deep |
| Measures of location, dispersion, skewness and kurtosis | Descriptive Statistics Unit 3 — Measures of Central Tendency Descriptive Statistics Unit 4 — Measures of Dispersion Descriptive Statistics Unit 5 — Moments, Skewness & Kurtosis | deep |
| Bivariate and multivariate data; association and contingency | Statistical Methods Unit 5 — Theory of Attributes | deep |
| Curve fitting and orthogonal polynomials | Statistical Methods Unit 1 — Curve Fitting | deep |
| Bivariate normal distribution | Multivariate Analysis Unit 1 — Multinomial and Multivariate Normal Distributions | deep |
| Regression — linear, polynomial | Statistical Methods Unit 4 — Regression | deep |
| Distribution of the correlation coefficient | Multivariate Analysis Unit 2 — Wishart Distribution, Generalized Variance and Correlation Distributions | deep |
| Partial and multiple correlation; intraclass correlation; correlation ratio | Statistical Methods Unit 3 — Concurrent Deviation, Multiple & Partial Correlation | deep |
| Standard errors and large sample tests | Inferential Statistics Unit 3 — Large Sample Tests | deep |
| Sampling distributions of sample mean, sample variance, t, chi-square and F; tests of significance based on them; small sample tests | Inferential Statistics Unit 4 — Small Sample Tests | deep |
| Non-parametric tests — goodness of fit, sign, median, run, Wilcoxon, Mann-Whitney, Wald-Wolfowitz and Kolmogorov-Smirnov | Inferential Statistics Unit 5 — Non-parametric Tests | deep |
| Concept of asymptotic relative efficiency | nothing on this site teaches it | not here |
7 syllabus lines: 0 taught in depth, 1 at exam level, 6 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Finite differences of different orders; Δ, E and D operators; factorial representation of a polynomial; separation of symbols; sub-division of intervals; differences of zero | nothing on this site teaches it | not here |
| Interpolation and extrapolation: Newton–Gregory forward and backward formulae for equal intervals; formula for unequal intervals | nothing on this site teaches it | not here |
| Central difference formulae due to Gauss, Stirling and Bessel; error terms in interpolation formulae | nothing on this site teaches it | not here |
| Inverse interpolation and the different methods for it | nothing on this site teaches it | not here |
| Numerical integration — Simpson's one-third and three-eighths rules, Weddle's rule | Actuarial Statistics — Practical | brief |
| Summation of series whose general term is a first difference, or in geometric progression | nothing on this site teaches it | not here |
| Numerical solution of differential equations — Runge–Kutta method | nothing on this site teaches it | not here |
5 syllabus lines: 1 taught in depth, 4 at exam level, 0 not here yet.
| Syllabus line, as prescribed | Where it is taught here | Depth |
|---|---|---|
| Basics of a computer: operations, central processing unit, memory, arithmetic and logical unit, input and output units; hardware and peripherals | Data Science Computer Fundamentals and Office Automation | brief |
| Software, system and application software; number systems; operating systems; packages and utilities; low and high level languages; compiler, assembler; RAM, ROM, units of memory | Data Science Computer Fundamentals and Office Automation | brief |
| Networks — LAN, WAN, internet, intranet; basics of computer security, virus, antivirus, firewall, spyware, malware | Data Science Computer Fundamentals and Office Automation | brief |
| Algorithm, flowchart, data, information, database; overview of programming languages; front end and back end of a project | Data Science Database Management Systems | brief |
| Variables, control structures, arrays and their usages, functions, modules, loops, conditional statements, exceptions, debugging | Data Science Python Programming and Data Structures | deep |
Not covered yet — 7 lines in Paper I. Read these from a standard text; this site does not yet teach them.