# GATE-2021 Statistics (ST)

In the year 2019, Statistics was added as a new subject in GATE. GATE 2021 Statistics Syllabus has been revised with the addition of some new topics like Matrix Theory, Testing of Hypotheses, etc. GATE aspirants must go through the revised syllabus to prepare for the exam and ace it with ease.

• The topics in GATE Statistics paper are based on the graduation level syllabus. The syllabus does not include Engineering Mathematics topics.
• The weightage of the core syllabus is 90% and the remaining 10% is of General Aptitude.

Mathematics

1. Calculus
2. Linear Algebra

Statistics

1. Probability
2. Stochastic Processes
3. Estimation
4. Testing of Hypothesis
5. Non-parametric Statistics
6. Multivariate Analysis
7. Regression Analysis

 Section No. of Question Type of Question Weightage of Marks General Aptitude (GA) 10 Single Choice Question(SCQ) 1 or 2 Mark(s) each Q.1-5 (1 Marks) Q.6-10(2 Marks) MA+ST Mathematics Statistics Mathematics 20%  of  55 Question Statistics 80%  of  55 Question 55     10-12     40-45 Single Choice Question(SCQ) Numerical Answer Type(NAT) 1 or 2 Mark(s) each Q.1-25 (1 Marks) Q.26-55(2 Marks)     Max. Marks: 100

GATE 2021 Syllabus for Statistics

Below given is a detailed syllabus of GATE STATISTICS paper:

Mathematics

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.

Linear Algebra

• Subspaces of  and , 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  and , 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.

Statistics

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

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.

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, converage probability.

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.

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.

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.

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.

GATE 2021 Exam Pattern of Statistics

GATE marks are distributed according to the guidelines formulated by the conducting body of the exam. While preparing for GATE ST, candidates should have good knowledge about GATE Exam Pattern.

• Mode of Examination: Online
• Duration of Exam: 3 hours
• Types of questions: MCQ and NATs (Numerical Answer Type)
• Total Sections: 2 Sections – General Aptitude, Mathematics and Statistics Subject-based
• No. of questions: 65 questions
• Total marks: 100 marks
• Negative marking: Only for MCQ

GATE Preparation Tips for GATE 2021 Statistics (ST) Paper

Practice Papers: With the help of papers of previous years or model test papers candidates can get an idea about the weightage of the questions, type of questions, important topics, etc. Candidates are advised to solve the questions from previous years’ papers after completion of each topic.

Mock Tests: Mock Tests are online tests and they give the feel of the real exam. you can check your level of preparation, accuracy, and speed while attempting the mock test. Candidates are suggested to go for the mock test only after the completion of whole syllabus.

Opportunity after qualify GATE Exam

After qualifying GATE 2021 candidates will be to get admission in M.Tech, Ph.D programs offered by prestigious institutes like IITs, NIts, etc. Other than admission to M.Tech courses, candidates can also apply for PSU recruitment through GATE offered by various PSUs. To prepare well for the exam candidates are advised to go through the article to know more about the syllabus, exam pattern, markings scheme, some preparation tips, and important books.

Thank-You

Regards

Pankaj Kumar

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