GATE Statistics 2027 Syllabus: Complete 12 Section Breakdown with PDF Download

The GATE Statistics 2027 syllabus, paper code ST, has been revised by IIT Madras and is now organised into 12 sections instead of 10. The sections are Calculus, Matrix Theory, Probability, Standard Univariate Distributions, Joint Distributions, Convergence of Random Variables, Stochastic Processes, Estimation, Testing of Hypotheses, Non Parametric Statistics, Multivariate Analysis and Regression Analysis. The paper carries 100 marks, with 15 marks from General Aptitude and 85 marks from Statistics, across 65 questions in 3 hours. The official syllabus PDF can be downloaded from the GATE 2027 website.

Download the Official GATE Statistics 2027 Syllabus

Straight from the IIT Madras GATE 2027 website. No sign up, no redirect.

Download ST Syllabus PDF

Download General Aptitude PDF

Most students download the syllabus PDF, glance at it once, and never open it again. That is the wrong way to use it. The GATE ST syllabus is not a document to read. It is a checklist to tick off, one topic at a time, over the next five months.

This page gives you the complete GATE Statistics 2027 syllabus broken into all 12 sections with every sub topic listed, grouped into four preparation blocks, and a clear list of what is not in the syllabus so you stop wasting time on chapters that will never be tested.

The 12 Section Structure at a Glance

The GATE 2027 notification confirms that the syllabi of the test papers have been revised. For Statistics, the change is structural. Joint Distributions and Convergence of Random Variables, which previously sat inside the distributions block, are now listed as separate named sections.

No.	Section	Nature of the Section
1	Calculus	Mathematical foundation
2	Matrix Theory	Mathematical foundation
3	Probability	Core probability
4	Standard Univariate Distributions	Core probability
5	Joint Distributions	Core probability
6	Convergence of Random Variables	Core probability
7	Stochastic Processes	Applied probability
8	Estimation	Statistical inference
9	Testing of Hypotheses	Statistical inference
10	Non Parametric Statistics	Statistical inference
11	Multivariate Analysis	Advanced statistics
12	Regression Analysis	Advanced statistics

If you want the full detail on how the 2027 structure differs from 2026, read our dedicated comparison: GATE ST Syllabus 2026 vs 2027.

Four Preparation Blocks

Twelve sections is a lot to hold in your head. Grouping them into four blocks makes the paper far easier to plan around, because it shows you which sections depend on which.

Block	Sections	Why It Comes First or Last
Block 1: Mathematical Foundation	Calculus, Matrix Theory	Everything else borrows from here. Weak foundations quietly cost you marks in four other sections.
Block 2: Probability Foundation	Probability, Standard Univariate Distributions, Joint Distributions, Convergence	The largest block. It feeds directly into inference and stochastic processes.
Block 3: Statistical Inference	Estimation, Testing of Hypotheses, Non Parametric Statistics	The conceptual heart of the paper. Cannot be attempted before Block 2 is solid.
Block 4: Applied and Advanced	Stochastic Processes, Multivariate Analysis, Regression Analysis	Each one combines probability with matrices or inference. Study these last.

The practical rule. Do not start Multivariate Analysis before Matrix Theory and Joint Distributions are comfortable. Do not start Estimation before Distributions are comfortable. Students who ignore this order end up re studying the same sections twice.

Complete Section Wise GATE Statistics 2027 Syllabus

Section 1: Calculus

Unit	Topics
Sets and Sequences	Finite, countable and uncountable sets. Convergence of sequences. Bounded and monotonic sequences. Cauchy criterion.
Infinite Series	Convergence tests. Alternating series. Absolute and conditional convergence. Power series and radius of convergence.
Functions of a Real Variable	Limits. Continuity. Uniform continuity. Differentiability. Rolle’s theorem. Mean Value Theorems. Taylor’s theorem. L’Hospital’s rule. Maxima and minima.
Integration	Riemann integration. Improper integrals.
Multivariable Calculus	Partial derivatives. Directional derivatives. Gradient. Total derivative. Taylor expansion. Maxima and minima. Saddle points. Lagrange multipliers.
Multiple Integration	Double integrals. Triple integrals. Applications of multiple integration.

Where it shows up in the paper. Calculus rarely appears as a standalone question in large numbers. It appears inside probability density transformations, maximum likelihood estimation, marginalisation of joint densities and optimisation problems. Improper integrals in particular appear constantly when you compute expectations of continuous distributions.

Section 2: Matrix Theory

Area	Topics
Vector Spaces	Subspaces. Span. Linear independence. Basis and dimension.
Matrix Structure	Row space. Column space. Rank. Nullity. Row reduced echelon form.
Matrix Operations	Trace. Determinant. Inverse. Systems of linear equations.
Inner Products	Inner products. Gram Schmidt orthonormalization.
Eigen Theory	Eigenvalues. Eigenvectors. Characteristic polynomial. Cayley Hamilton theorem.
Special Matrices	Symmetric. Skew symmetric. Hermitian. Skew Hermitian. Orthogonal. Unitary.
Transformations	Change of basis. Similarity. Diagonalizability.
Quadratic Forms	Positive definite and positive semi definite matrices.
Decomposition	Singular Value Decomposition.

Note on Singular Value Decomposition. SVD is specific to GATE ST and is not part of the IIT JAM MS syllabus. If you are switching from JAM preparation, this is one topic you will have to add from scratch.

Section 3: Probability

• Axiomatic definition of probability and its properties
• Conditional probability
• Bayes’ theorem
• Independence
• Random variables
• Cumulative Distribution Function, Probability Mass Function and Probability Density Function
• Expectation and variance
• Moments
• Moment Generating Function
• Probability Generating Function
• Quantiles
• Functions of random variables
• Markov inequality
• Chebyshev inequality
• Jensen inequality

Section 4: Standard Univariate Distributions

Type	Distributions
Discrete	Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric, Discrete Uniform, Poisson
Continuous	Continuous Uniform, Exponential, Double Exponential, Gamma, Beta Type I, Beta Type II, Weibull, Normal, Cauchy

That is sixteen distributions. Build a single revision chart covering all of them with support, PMF or PDF, mean, variance, MGF or PGF, parameter restrictions and relationships to other distributions. One chart replaces hours of last month panic.

Section 5: Joint Distributions

• Joint CDF, PMF and PDF
• Marginal distributions
• Conditional distributions and conditional expectation
• Conditional moments
• Product moments and correlation coefficient
• Joint Moment Generating Function
• Independence of random variables
• Functions of random vectors and transformations
• Order statistics, including joint and marginal distributions of order statistics
• Multinomial distribution
• Bivariate normal distribution
• Sampling distributions
• Central chi square, central t and central F distributions

Section 6: Convergence of Random Variables

• Convergence in distribution
• Convergence in probability
• Almost sure convergence
• Convergence in r-th mean
• Relationships among the modes of convergence
• Slutsky’s lemma
• Borel Cantelli lemma
• Weak Law of Large Numbers
• Strong Law of Large Numbers
• Central Limit Theorem for independent and identically distributed random variables

This section is short on the page and heavy in the exam. The questions usually test whether you know which mode of convergence implies which, and whether a given counterexample breaks the implication. Learn the implication diagram cold.

Section 7: Stochastic Processes

Area	Topics
Markov Chains	Finite and countable state spaces
Classification of States	Transient, recurrent, periodic and absorbing states
Transition Behaviour	Limiting behaviour of n-step transition probabilities
Stationarity	Stationary distributions
Poisson Process	Basic properties and applications
Birth and Death Processes	Birth and death, pure birth and pure death processes
Brownian Motion	Basic properties

Section 8: Estimation

• Sufficiency and minimal sufficiency
• Factorization theorem
• Completeness and complete exponential families
• Ancillary statistics
• Basu’s theorem
• Unbiased estimation
• Uniformly Minimum Variance Unbiased estimation
• Rao Blackwell theorem
• Lehmann Scheffe theorem
• Cramer Rao inequality
• Consistency
• Method of Moments
• Maximum Likelihood Estimation and properties of the MLE
• Pivotal quantities
• Confidence intervals and coverage probability

Section 9: Testing of Hypotheses

• Null and alternative hypotheses
• Type I and Type II errors
• Power function
• Neyman Pearson lemma
• Most Powerful tests
• Monotone Likelihood Ratio property
• Uniformly Most Powerful tests and UMP tests for MLR families
• Uniformly Most Powerful Unbiased tests and UMPU tests for exponential families
• Likelihood Ratio Tests
• Large sample tests

Section 10: Non Parametric Statistics

• Empirical Distribution Function
• Goodness of fit tests
• Chi square test
• Kolmogorov Smirnov test
• Run tests
• Sign test
• Wilcoxon signed rank test
• Mann Whitney U test
• Kruskal Wallis test
• Spearman rank correlation
• Kendall rank correlation

This is the most procedurally predictable section in the paper. Each test has a fixed statistic, a fixed null distribution and a fixed decision rule. Students who make a one page summary table of all eleven items above tend to convert this section into reliable marks.

Section 11: Multivariate Analysis

• Multivariate normal distribution and its properties
• Conditional distributions of the multivariate normal
• Marginal distributions of the multivariate normal
• Maximum likelihood estimation of the mean vector
• Maximum likelihood estimation of the dispersion matrix
• Hotelling’s T squared test
• Wishart distribution and its basic properties
• Multiple correlation coefficient
• Partial correlation coefficient

Section 12: Regression Analysis

• Simple linear regression
• Multiple linear regression
• Least squares estimation
• R squared and adjusted R squared, and their applications
• Quadratic forms of random vectors
• Fisher Cochran theorem
• Gauss Markov theorem
• Tests for regression coefficients
• Confidence intervals

A Syllabus Is a Checklist, Not a Study Plan

Chakravyuh Mock turns these 12 sections into a practice schedule. Topic wise tests as you finish each section, full length mocks on the real ST interface with the virtual calculator, all eight ST previous year papers, and All India Rank in every test.

See Everything Inside Chakravyuh Mock

What Is NOT in the GATE Statistics 2027 Syllabus

This section saves more time than any other on this page. A large number of Statistics students prepare topics that simply are not tested in GATE ST, usually because those topics were part of their university course or another examination they are also preparing for.

The following are not in the GATE ST 2027 syllabus. Do not spend time on them for this paper.

• Descriptive statistics, measures of central tendency and dispersion
• Index numbers
• Time series analysis
• Sampling theory and survey sampling techniques
• Design of experiments and analysis of variance as a standalone topic
• Vital statistics and demography
• Statistical quality control
• Bayesian inference and decision theory
• Sequential analysis
• Official statistics and the Indian statistical system
• Operations research and linear programming
• Principal Component Analysis, Factor Analysis and Discriminant Analysis

An important clarification. Several of these topics appear in UPSC ISS and UGC NET Statistics. If you are preparing for more than one examination, keep separate checklists. Studying official statistics or sampling theory will not earn you a single mark in GATE ST.

Also note that quadratic forms and the Fisher Cochran theorem do appear inside Regression Analysis. That is not the same as a full ANOVA and design of experiments syllabus.

General Aptitude Syllabus for GATE Statistics

General Aptitude is common across all 30 GATE papers and carries 15 marks across 10 questions. It covers:

• Verbal Aptitude: basic English grammar, vocabulary, reading comprehension, narrative sequencing
• Quantitative Aptitude: data interpretation, numerical computation, ratios, percentages, mensuration, elementary statistics and probability
• Analytical Aptitude: logic, deduction and induction, analogy, numerical relations
• Spatial Aptitude: transformation of shapes, paper folding and cutting, patterns in two and three dimensions

Fifteen marks is 15 percent of the paper for a section that needs perhaps three weeks of total preparation. Students who skip it entirely are giving away the cheapest marks on the paper.

How to Use This Syllabus as a Checklist

Here is the method that actually works, and it takes about twenty minutes to set up.

1. Print the syllabus or paste it into a spreadsheet. One row per sub topic. You will end up with roughly 110 rows.
2. Add four columns: Theory Done, Questions Solved, PYQ Done, Revised.
3. Never tick Theory Done alone. A topic is not finished until at least the second column is ticked too. Reading without solving creates a false sense of preparation, and it is the single most common failure pattern in GATE ST.
4. Tick PYQ Done immediately after each topic, not at the end of the syllabus. Previous year questions are a learning tool, not a final exam rehearsal.
5. Review the sheet every Sunday. Rows with only the first column ticked are your weakest points, and they will be the ones that cost you marks in February.

This one sheet answers the question every aspirant asks in December: what exactly is left. Practice. Improve. Repeat. That loop only works when you can see where you are in it.

Frequently Asked Questions

Related Reading

• GATE Statistics 2027 Exam Dates and Registration
• GATE ST Syllabus 2026 vs 2027
• Best Books for GATE Statistics 2027
• GATE Statistics Previous Year Papers