GATE 2025 Statistics Syllabus (Available) – Get (ST) Syllabus PDF Here

The GATE 2025 Syllabus for Statistics has been officially released by IIT Roorkee. This national-level examination plays a crucial role in granting admission to postgraduate programs in engineering and technology, particularly ME/M.Tech. The newly released syllabus for Statistics outlines the key topics and areas of focus for candidates preparing for the exam.

The GATE 2025 exam is scheduled to take place on the 1st, 2nd, 15th, and 16th of February 2025. The Statistics syllabus covers a comprehensive range of subjects, including probability theory, statistical inference, regression analysis, and design of experiments. This extensive coverage ensures that candidates are well-prepared to handle both theoretical and practical aspects of Statistics in their postgraduate studies.

For the most accurate and detailed information about the GATE 2025 syllabus for Statistics, candidates should refer to the official guidelines provided by IIT Roorkee. Adequate preparation based on this syllabus will be essential for achieving a competitive score and advancing in the field of Statistics.

GATE 2025 Statistics Syllabus – PDF Released

GATE 2025 Statistics Syllabus

Calculus: Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property; Sequences and series, convergence; Limits, continuity, uniform continuity, differentiability, mean value theorems; Riemann integration, Improper integrals; Functions of two or three variables, continuity, directional derivatives, partial derivatives, total derivative,

maxima and minima, saddle point, a method of Lagrange’s multipliers; Double and Triple integrals and their applications; Line integrals and Surface
integrals, Green’s theorem, Stokes’, and Gauss’s divergence theorem.

Linear Algebra: Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan canonical form,

symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices; Finite dimensional inner product spaces, Gram- Schmidt orthonormalization process, definite forms.

Probability: Classical, relative frequency and axiomatic definitions of probability, conditional probability, Bayes’ theorem, independent events; Random variables and probability distributions, moments and moment generating functions, quantiles; Standard discrete and continuous univariate distributions;

Probability inequalities (Chebyshev, Markov, Jensen); Function of a random variable; Jointly distributed random variables, marginal and conditional distributions, product moments, joint moment generating
functions, independence of random variables; Transformations of random variables, sampling distributions, distribution of order statistics and range; Characteristic functions; Modes of convergence; Weak and strong laws of large numbers; Central limit theorem for I .i.d. random variables with the existence of higher-order moments.

Stochastic Processes: Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution, Poisson, and birth-and-death processes.

Inference: Unbiasedness, consistency, sufficiency, completeness, uniformly minimum variance unbiased estimation, method of moments and maximum likelihood estimations; Confidence intervals; Tests of hypotheses, most powerful and uniformly most powerful tests, likelihood ratio tests, large sample test, Sign test, Wilcoxon signed-rank test, Mann- Whitney U test, test for independence and Chi-square test for goodness of fit.

Regression Analysis: Simple and multiple linear regression, polynomial regression, estimation, confidence intervals, and testing for regression coefficients; Partial and multiple correlation coefficients.

Multivariate Analysis: Basic properties of the multivariate normal distribution; Multinomial distribution; Wishart distribution; Hotelling’s T2 and related tests; Principal component analysis; Discriminant analysis; Clustering.

Design of Experiments: One and two-way ANOVA, CRD, RBD, LSD, 22, and 23 Factorial Experiments.

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Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigenvalues and eigenvectors.

Calculus: Limit, continuity, and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.

Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green’s theorems.

Differential Equations: Linear and non-linear first-order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs -Laplace, heat and wave equations.

Probability and Statistics: Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.

Numerical Methods: Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.

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Sunil Kushwaha

As a dedicated Biology Science graduate, I’m passionate about sharing the latest updates in national and state entrance exams through my blog. I aim to keep aspiring students informed about exam trends, important dates, and changes in syllabi. With a keen interest in education, I strive to offer valuable insights for students navigating the competitive landscape of entrance examinations and admission tests. Stay updated with me.