GATE Statistics Syllabus 2022 and Exam Pattern | Books, Weightage

GATE Statistics Syllabus 2022: IIT Kharagpur is the conducting authority for GATE Exam 2022. To plan and prepare properly for the exam, you must have latest GATE Syllabus 2022 and exam pattern.

The syllabus includes all the major topics of the graduate level but does not include Engineering Mathematics as a topic. The most important Topic in the GATE Statistics Syllabus is Probability as it comprises almost 20% of the total weightage in the GATE Paper.

To know more about the GATE Statistics Syllabus and Exam Pattern 2022, read the whole blog.

GATE Statistics Syllabus 2022

GATE Statistics Syllabus 2022 consists of 9 different sections, Calculus, Matrix Theory, Probability, Stochastic process, Estimation, Testing of hypothesis, Nonparametric Statistics, Multivariate Analysis and Regression Analysis.

Candidates with Statistics (ST) as their first paper can only opt one paper from either Mathematics (MA) or Physics (PH) as their second paper. However, it is not mandatory that you have to appear for 2 papers.

Here you can check detailed GATE Statistics Syllabus 2022.

Section 1: Calculus

• Finite, countable and uncountable sets; Real number system as a complete ordered field, Archimedean property; 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 Rnn and Cnn, 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 Rnn and Cnn, Gram-Schmidt orthonormalization
• Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, symmetric, skew-symmetric, Hermitian, skew-Hermitian, 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, 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, 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.
• 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 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.
• 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, delta method.

Section 4: 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 5: 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 6: 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 7: Non-parametric Statistics

• Empirical distribution function and its properties, 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.

Section 8: 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 9: 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.

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GATE Statistics Syllabus 2022 On General Aptitude 

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GATE Statistics Exam Pattern 2022

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Topic-wise Weightage For GATE Statistics Syllabus 2022

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Reference Books Based On Latest GATE Statistics Syllabus 2022

You must select the correct books to study for GATE 2022 preparation. You can check the list of referred books for Statistics. By referring to these books, you can boost your preparation process.

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