GATE Statistics Syllabus 2026

GATE Statistics syllabus 2026 is divided into General Aptitude and Statistics topics. The core syllabus accounts for 85% of the weightage, with General Aptitude accounting for the remaining 15%. It is divided into nine sections, which are as follows:

• Calculus
• Matrix Theory
• Probability
• Stochastic process
• Estimation
• Testing of hypothesis
• Non-parametric Statistics
• Multivariate Analysis
• Regression Analysis

Note: Probability is the most important topic in the GATE Statistics Syllabus, accounting for nearly 20% of the total weightage in the GATE Paper.

Calculus: Calculus section of the GATE Statistics syllabus 2026 includes a variety of important topics such as alternating series, L' Hospital rules, maxima and minima, and so on. Let us now go over these topics in greater depth.

• Countable and uncountable finite sets; Real number system as a fully ordered field, according to the Archimedean principle; real number sequences, the convergence of sequences, limited sequences, monotonic sequences, and the Cauchy convergence criterion; Real number series, absolute and conditional convergence, tests for convergence, and alternating series.
• Power series and the radius of convergence; Real variable functions such as limit, continuity, monotone functions, uniform continuity, differentiability, Rolle's theorem, mean value theorems, Taylor's theorem, L'Hospital rules, maxima and minima, Riemann integration and its properties, and improper integrals.
• Limit, continuity, partial derivatives, directional derivatives, gradient, Taylor's theorem, total derivative, maxima and minima, saddle point, method of Lagrange multipliers, double and triple integrals, and their applications are all functions of multiple real variables.

Matrix Theory: Matrix Theory section of the GATE Statistics syllabus 2026 includes several important topics such as Rnn, Cnn, and quadratic forms. Let us now go over these topics in greater depth.

• Rnn and Cnn subspaces; span; linear independence; basis and dimension; the row reduced echelon form; trace and determinant; the inverse of a matrix; linear equation systems; inner products in Rnn and Cnn; and Gram-Schmidt orthonormalization.
• Eigenvalues and eigenvectors, Cayley-Hamilton theorem, orthogonal, unitary matrices and their eigenvalues, change of basis matrix, equivalence and similarity, diagonalizability, positive definite and positive semi-definite matrices and their properties, quadratic forms, and singular value decomposition

Probability: Probability section of the GATE Statistics syllabus 2026 covers a wide range of important topics, including the probability density function, Bayes' theorem, Chebyshev, and others. Let's take a look at the topics listed below.

• Random variables and their distributions, distribution function, probability mass function, probability density function and their properties, expectation, moments and moment generating function, quantiles, distribution of functions of a random variable, Chebyshev, Markov, and Jensen inequalities are just a few of the topics covered.
• Standard discrete and continuous univariate distributions: Bernoulli, binomial, geometric, negative binomial, hypergeometric, discrete uniform, Poisson, continuous uniform, exponential, gamma, beta, Weibull, normal.
• Jointly distributed random variables and their distribution functions; probability mass and density functions and their characteristics; marginal and conditional distributions; conditional expectation and moments; product moments; simple correlation coefficient; independence of random variables; functions of random vector and their distributions; distributions of order statistics; joint and marginal distributions of order s.
• Distribution convergence, probability convergence, almost certain convergence, r-th mean convergence, and their interrelationships Slutsky's lemma, the Borel-Cantelli lemma, the weak and strong laws of large numbers, the central limit theorem for i.i.d. random variables, and the delta method

Stochastic process: Stochastic process section of the GATE Statistics syllabus 2026 includes topics such as pure-birth process, Poisson process, state classification, and so on. Let us now go over these topics in greater depth.

• Markov chains with finite and countable state space, classification of states, limiting behavior of n-step transition probabilities, stationary distribution.
• Poisson process, birth and death process, pure-birth process, pure-death process, Brownian motion, and its basic properties.

Estimation: Estimation section of the GATE Statistics syllabus 2026 covers a variety of important topics such as sufficiency, minimal sufficiency, completeness, completeness of exponential families, ancillary statistics, and so on. Candidates can find the topics listed below.

• Sufficiency, minimal sufficiency, factorization theorem, completeness, completeness of exponential families, ancillary statistic, Basu's theorem and its applications, unbiased estimation, uniformly minimum variance unbiased estimation, Rao-Blackwell theorem, Lehmann-Scheffe theorem, Rao-Blackwell theorem, Rao-Blackwell theorem, Rao-Blackwell theorem, Rao-Black
• The Cramer-Rao inequality, consistent estimators, method of moments estimators, method of maximum likelihood estimators, and their properties; Interval estimation: pivotal quantities and confidence intervals based on them, coverage probability

Testing of Hypothesis: Neyman-Pearson lemma, most powerful tests, the monotone likelihood ratio (MLR) property, uniformly most powerful tests, uniformly most powerful tests for families having the MLR property, uniformly most powerful unbiased tests, uniformly most powerful unbiased tests for exponential families, likelihood ratio tests, and large sample tests are just a few of the significant topics covered in the Testing of Hypothesis section of the GATE Statistics syllabus 2026.

Non-parametric Statistics: Empirical distribution function and its properties, the goodness of fit tests, chi-square test, Kolmogorov-Smirnov test, sign test, Wilcoxon signed rank test, Mann-Whitney U-test, rank correlation coefficients of Spearman and Kendall.

Multivariate Analysis: Multivariate normal distribution: properties, maximum likelihood estimation of mean vector and dispersion matrix, conditional and marginal distributions, Hotelling’s T2 test, Wishart distribution, and its basic properties, multiple and partial correlation coefficients, and their basic properties.

Regression Analysis: Simple and multiple linear regression, distributions of quadratic forms of random vectors, R2 and adjusted R2 and their applications: Fisher-Cochran theorem, Gauss-Markov theorem, tests for regression coefficients, confidence intervals.

GATE Statistics Syllabus 2026: Weightage of Important Topics

The general trend in the GATE Statistics test in terms of the weightage of the various disciplines is presented below based on the analysis of the Previous Year's GATE Chemistry Paper.

GATE Statistics Syllabus 2026: Exam Pattern

The organization in charge of delivering the GATE exam has set rules for how it will be graded. While preparing for the GATE ST, candidates should have a full understanding of the GATE Exam Pattern.

GATE 2026 Marking scheme

• Total Marks: 100 marks
• Negative Marking: For MCQs only

GATE 2026 Statistics Preparation Tips

One of the key subjects included on the GATE exam is statistics. Candidates should organize their study time in accordance with the exam format, weighting, and scoring system of the Statistics syllabus for the GATE. The preparation advice for applicants to complete and prepare the curriculum is provided below.

• Prepare a timetable.
• Focus on basic concepts.
• Understand the exam pattern and weightage of topics.
• Prepare notes on each topic.
• Practice previous year's question papers.

GATE Statistics Syllabus 2026: Best Books

The right books must be chosen by candidates to study for the GATE Statistics (ST) syllabus 2026. Additionally, they can increase their preparation by consulting the books listed in the table below: