GATE Statistics
- 3
- Years
- 3
- Papers
- 195
- Questions
Admission to M.Tech/PhD programmes and PSU recruitment. The ST paper tests calculus, matrix theory, probability and distributions, stochastic processes, estimation, testing, non-parametric methods, multivariate analysis and regression.
Exam pattern
- 65 questions, 100 marks, 3 hours: General Aptitude (Q1–10, 15 marks) + subject (Q11–65, 85 marks)
- MCQ (one correct option), MSQ (one or more correct, all-or-nothing) and NAT (type a number)
- Wrong MCQ answers cost 1/3 (1-mark) or 2/3 (2-mark); no negative marking for MSQ or NAT
- On-screen virtual scientific calculator only
The most recent paper solved here, GATE 2026 Statistics (ST), ran to 65 questions: 10 in Section GA and 55 in Section ST.
Conducted by IISc and the IITs (organising institute rotates). Patterns change from year to year, so confirm the current one at gate2027.iitm.ac.in.
Topic analysis
How many questions each syllabus topic and subtopic was worth, year by year, across the 3 solved GATE ST papers (195 questions). Sittings of the same year are counted together.
| Topic · subtopic | 2026 | 2025 | 2024 | Total |
|---|---|---|---|---|
| Probability | 9 | 8 | 11 | 28 |
| Distribution of functions of a random variable | 4 | 3 | 4 | 11 |
| Moments and moment generating function | 1 | 2 | 3 | 6 |
| Properties of probability function | 1 | 1 | 3 | 5 |
| Cumulative distribution function | 2 | 1 | · | 3 |
| Independence of events; Random variables and their distributions | 1 | · | 1 | 2 |
| Properties of expectation and variance | · | 1 | · | 1 |
| Testing of Hypotheses | 7 | 6 | 9 | 22 |
| Most powerful tests | 5 | 3 | 3 | 11 |
| Uniformly most powerful unbiased tests for exponential families | · | · | 4 | 4 |
| Likelihood ratio tests | 1 | 1 | 1 | 3 |
| Neyman-Pearson lemma | · | 2 | 1 | 3 |
| Uniformly most powerful tests for families having MLR property | 1 | · | · | 1 |
| Matrix Theory | 7 | 7 | 7 | 21 |
| Inverse of a matrix | 1 | 2 | 1 | 4 |
| Diagonalizability | 1 | · | 1 | 2 |
| Inner products in ℝ𝑛 and ℂ𝑛, Gram-Schmidt orthonormalization | 1 | · | 1 | 2 |
| Rank and nullity | · | 2 | · | 2 |
| Subspaces of ℝ𝑛 and ℂ𝑛 | 1 | · | 1 | 2 |
| Systems of linear equations; Inner products in ℝ𝑛 and ℂ𝑛 | 2 | · | · | 2 |
| Trace and determinant | · | 2 | · | 2 |
| Characteristic polynomial | · | · | 1 | 1 |
| Quadratic forms | 1 | · | · | 1 |
| Row space and column space of a matrix | · | · | 1 | 1 |
| Singular value decomposition | · | · | 1 | 1 |
| Skew-symmetric | · | 1 | · | 1 |
| Estimation | 9 | 6 | 5 | 20 |
| Unbiased estimation | 3 | 2 | 3 | 8 |
| Minimal sufficiency | 2 | 2 | · | 4 |
| Method of maximum likelihood estimators and their properties; pivotal quantities and confidence intervals based on them | 1 | 1 | 1 | 3 |
| Cramer-Rao inequality | 1 | 1 | · | 2 |
| Method of moments estimators | 2 | · | · | 2 |
| Ancillary statistic | · | · | 1 | 1 |
| Calculus | 7 | 7 | 5 | 19 |
| Functions of several real variables | 2 | 2 | 2 | 6 |
| Series of real numbers, convergence, tests of convergence, alternating series, absolute and conditional convergence | 2 | 3 | 1 | 6 |
| Power series and radius of convergence | 1 | 1 | 1 | 3 |
| Functions of a real variable | 1 | · | 1 | 2 |
| Finite, countable and uncountable sets | · | 1 | · | 1 |
| Sequences of real numbers, convergence of sequences, bounded sequences, monotonic sequences, Cauchy criterion for convergence | 1 | · | · | 1 |
| Quantitative Aptitude | 4 | 4 | 6 | 14 |
| Basic probability | 1 | · | · | 1 |
| Counting | 1 | · | · | 1 |
| Data interpretation | · | · | 1 | 1 |
| Linear constraints | 1 | · | · | 1 |
| Linear equations | · | 1 | · | 1 |
| Logarithms | · | · | 1 | 1 |
| Mixture and alligation | · | 1 | · | 1 |
| Number puzzles | · | 1 | · | 1 |
| Number series | · | · | 1 | 1 |
| Permutations | · | · | 1 | 1 |
| Piecewise functions | 1 | · | · | 1 |
| Profit and loss | · | · | 1 | 1 |
| Set theory | · | · | 1 | 1 |
| Unitary method | · | 1 | · | 1 |
| Multivariate Analysis | 5 | 6 | 2 | 13 |
| Multivariate normal distribution | 4 | 6 | 1 | 11 |
| Wishart distribution and its basic properties | 1 | · | 1 | 2 |
| Stochastic Processes | 3 | 3 | 5 | 11 |
| Markov chains with finite and countable state space | 1 | 1 | 2 | 4 |
| Poisson process | 1 | 1 | 2 | 4 |
| Brownian motion and its basic properties | 1 | 1 | 1 | 3 |
| Joint Distributions | 3 | 4 | 3 | 10 |
| Joint and marginal distributions of order statistics; multinomial distribution | 1 | 2 | 1 | 4 |
| Simple correlation coefficient | 1 | 1 | · | 2 |
| Bivariate normal distribution | · | · | 1 | 1 |
| Distributions of order statistics | 1 | · | · | 1 |
| Joint moment generating function | · | · | 1 | 1 |
| Sampling distributions: central chi-square | · | 1 | · | 1 |
| Regression Analysis | 1 | 4 | 5 | 10 |
| Simple and multiple linear regression | 1 | 4 | 5 | 10 |
| Convergence of Random Variables | 2 | 4 | 3 | 9 |
| Convergence in distribution | · | 2 | · | 2 |
| Convergence in 𝑟 − 𝑡ℎ mean and their inter-relations | · | · | 2 | 2 |
| Borel-Cantelli lemma; weak and strong laws of large numbers; central limit theorem for i.i.d. random variables | 1 | · | · | 1 |
| Central limit theorem for i.i.d | · | · | 1 | 1 |
| Convergence almost surely | · | 1 | · | 1 |
| Random variables | 1 | · | · | 1 |
| Weak and strong laws of large numbers | · | 1 | · | 1 |
| Verbal Aptitude | 1 | 3 | 2 | 6 |
| Phrasal verbs | · | 1 | · | 1 |
| Reading comprehension | · | 1 | · | 1 |
| Sentence sequencing | · | · | 1 | 1 |
| Subject-verb agreement | · | 1 | · | 1 |
| Word analogy | · | · | 1 | 1 |
| Word meaning | 1 | · | · | 1 |
| Spatial Aptitude | 2 | 2 | 1 | 5 |
| 3D cutting | · | · | 1 | 1 |
| Geometry | · | 1 | · | 1 |
| Matrix puzzles | · | 1 | · | 1 |
| Orthographic projection | 1 | · | · | 1 |
| Pattern construction | 1 | · | · | 1 |
| Analytical Aptitude | 3 | 1 | 1 | 5 |
| Coding-decoding | · | 1 | · | 1 |
| Deductive reasoning | 1 | · | · | 1 |
| Grid logic | · | · | 1 | 1 |
| Logical inference | 1 | · | · | 1 |
| Passage-based inference | 1 | · | · | 1 |
| Standard Univariate Distributions | 1 | 1 | ||
| Beta distributions of first and second kinds | 1 | · | · | 1 |
| Non-parametric Statistics | 1 | 1 | ||
| Empirical distribution function and its properties | 1 | · | · | 1 |
| All topics | 65 | 65 | 65 | 195 |
Syllabus
From the IISc and the IITs (organising institute rotates) GATE 2027 ST syllabus. Always check it against the current notification.
Section 1
Calculus
Finite, countable and uncountable sets; Sequences of real numbers, convergence of sequences, bounded sequences, monotonic sequences, Cauchy criterion for convergence; Series of real numbers, convergence, tests of convergence, alternating series, absolute and conditional convergence; Power series and radius of convergence; Functions of a real variable: 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, improper integrals; Functions of several real variables: 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.
Section 2
Matrix Theory
Subspaces of ℝ𝑛 and ℂ𝑛, span, linear independence, basis and dimension, row space and column space of a matrix, rank and nullity, row reduced echelon form, trace and determinant, inverse of a matrix, systems of linear equations; Inner products in ℝ𝑛 and ℂ𝑛, Gram-Schmidt orthonormalization; Eigen values and eigen vectors, characteristic polynomial, Cayley-Hamilton theorem, symmetric, skew-symmetric, Hermitian, skewHermitian, orthogonal, unitary matrices and their eigen values, change of basis matrix, equivalence and similarity, diagonalizability, positive definite and positive semi-definite matrices and their properties, quadratic forms, singular value decomposition.
Section 3
Probability
Axiomatic definition of probability, properties of probability function, conditional probability, Bayes' theorem, independence of events; Random variables and their distributions, cumulative distribution function, probability mass function, probability density function and their properties, expectation, variance, properties of expectation and variance, moments and moment generating function, probability generating function, quantiles, distribution of functions of a random variable, Chebyshev, Markov and Jensen inequalities.
Section 4
Standard Univariate Distributions
Bernoulli, binomial, geometric, negative binomial, hypergeometric, discrete uniform, Poisson, continuous uniform, exponential, double exponential, gamma, beta distributions of first and second kinds, Weibull, normal, Cauchy.
Section 5
Joint Distributions
Jointly distributed random variables and their distribution functions, probability mass function, probability density function and their properties, marginal and conditional distributions, conditional expectation and moments, product moments, simple correlation coefficient, joint moment generating function, independence of random variables, functions of random vector and their distributions, distributions of order statistics, 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, convergence almost surely, convergence in 𝑟 − 𝑡ℎ mean and their inter-relations, Slutsky's lemma, Borel-Cantelli lemma; weak and strong laws of large numbers; central limit theorem for i.i.d. random variables.
Section 7
Stochastic Processes
Markov chains with finite and countable state space, classification of states, limiting behaviour 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.
Section 8
Estimation
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, 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.
Section 9
Testing of Hypotheses
Neyman-Pearson lemma, most powerful tests, monotone likelihood ratio (MLR) property, uniformly most powerful tests, uniformly most powerful tests for families having MLR property, uniformly most powerful unbiased tests, uniformly most powerful unbiased tests for exponential families, likelihood ratio tests, large sample tests.
Section 10
Non-parametric Statistics
Empirical distribution function and its properties, 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, rank correlation coefficients of Spearman and Kendall.
Section 11
Multivariate Analysis
Multivariate normal distribution: properties, conditional and marginal distributions, maximum likelihood estimation of mean vector and dispersion matrix, Hotelling's 𝑇2 test, Wishart distribution and its basic properties, multiple and partial correlation coefficients and their basic properties.
Section 12
Regression Analysis
Simple and multiple linear regression, 𝑅2 and adjusted 𝑅2 and their applications, distributions of quadratic forms of random vectors: Fisher-Cochran theorem, Gauss-Markov theorem, tests for regression coefficients, confidence intervals.