  By BYJU'S Exam Prep

Updated on: October 17th, 2023 GATE Statistics syllabus 2023 will be released by IIT Kanpur on its official website with some newly added changes. Candidates who intend to prepare for the upcoming exam should review the most recent GATE Statistics syllabus to improve their chances of passing the exam.

GATE Statistics syllabus 2023 provides useful information that you need to know before preparing for the exam. Candidates are advised to go through the entire syllabus and find below the latest GATE Statistics syllabus PDF to crack the examThus, let us check the simplified syllabus along with other important topics that you must know.

## Detailed GATE Statistics Syllabus 2023

GATE Statistics syllabus 2023 is divided into General Aptitude and topics from Statistics. The weightage of the core syllabus is 85% and the remaining 15% is of General Aptitude. It consists of 9 different sections which are as follows:

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

Further, let us now discuss these different sections of the GATE syllabus for Statistics 2023 in detail.

## GATE Statistics Syllabus Calculus

The Calculus section of the GATE Statistics syllabus 2023 consists of various important topics such as alternating series, L’ Hospital rules, maxima, minima, etc. Further, let us discuss these topics in detail.

• Finite, countable, and uncountable sets; Real number system as a complete ordered field, Archimedean property; Sequences of real numbers, the 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.

## GATE Statistics Syllabus Matrix Theory

The Matrix Theory section of the GATE Statistics syllabus 2023 consists of various important topics included in the syllabus such as Rnn, Cnn, and quadratic forms. Further, let us discuss these topics in detail.

• 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.

## GATE Statistics Syllabus Probability

The Probability section of the GATE Statistics syllabus 2023 consists of various important topics such as probability density function, Bayes’ theorem, Chebyshev, etc. Let us check the topics listed in the table below.

 Axiomatic definition of probability Independence of events Bayes’ theorem Distribution of functions of a random variable Chebyshev, Markov, and Jensen’s inequalities Distribution function Probability density function and their properties Random variables and their distributions Expectation Quantiles Conditional probability Moments and moment generating function

## GATE Statistics Syllabus Stochastic process

The Stochastic process section of the GATE Statistics syllabus 2023 consists of the topics such as pure-birth process, Poisson process Classification of states etc. Further, let us discuss these topics in detail.

• 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.

## GATE Statistics Syllabus Estimation

The Estimation section of the GATE Statistics syllabus 2023 carries various important topics such as Sufficiency, minimal sufficiency, completeness, completeness of exponential families, ancillary statistics, etc. Candidates can find the topics listed in the table below.

 Coverage probability Method of moments estimators Interval estimation: pivotal quantities and confidence intervals Cramer-Rao inequality Unbiased estimation Uniformly minimum variance unbiased estimation Rao-Blackwell theorem Method of maximum likelihood estimators and their properties Lehmann-Scheffe theorem Completeness of exponential families Factorization theorem Sufficiency

## GATE Statistics Syllabus Testing of hypothesis

The Testing of hypothesis section of the GATE Statistics syllabus 2023 consists of various important topics which are the 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.

## GATE Statistics Syllabus Non-parametric Statistics

The Nonparametric Statistics section of the GATE Statistics syllabus 2023 the following topics- 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, In Rank-correlation In coefficients In of Spearman and Kendall.

## GATE Statistics Syllabus Multivariate Analysis

The Multivariate Analysis section of the GATE Statistics syllabus 2023 consists of the following topics- 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.

## GATE Statistics Syllabus Regression Analysis

The Regression Analysis section of the GATE Statistics syllabus 2023 constitutes various important topics such as 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, and confidence intervals.

The GATE syllabus for Statistics consists of 9 sections namely- Calculus, Matrix Theory, Probability, Stochastic process, Estimation, Testing of hypothesis, Non-parametric Statistics, Multivariate Analysis, and Regression Analysis. Candidates can download the entire syllabus from the PDF provided below.

## Preparation Tips for GATE Statistics Syllabus 2023

Statistics is one of the important topics of the GATE exam. In order to prepare the GATE syllabus for Statistics, candidates should plan their preparation according to the exam pattern, weightage, and marking scheme of the syllabus. Below we have provided the preparation tips for candidates to finish and prepare the syllabus.

• 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.

## Best books for GATE Statistics Syllabus 2023

Candidates must select the correct books to study for GATE Statistics (ST) syllabus 2023. Further, they can refer to the books listed in the table below to boost their preparation.

 Name of Books Author Programmed Statistics B. L. Agarwal Probability Athanasios Papoulis Fundamentals of Statistics S. C. Gupta Mathematical Statistics J. N. Kapur

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