 # GATE Statistics Syllabus

GATE 2022 Statistics Syllabus– IIT Kharagpur releases the subject or branch wise official syllabus on the website. Meanwhile, here in this article or the webpage, we have compiled the PDF version and the details of the GATE Syllabus for Statistics.

To get an idea about the contents and topics that will be asked in the question paper, candidates can browse through this web page and analyse the GATE syllabus. Hence, candidates can click on the link provided below to access the PDF format of the GATE syllabus for Statistics.

## GATE 2022 Statistics Syllabus

Below, please find the topics and sub-topics covered for the exams in the selected subject as per the GATE 2022 Syllabus for Statistics. Find some main topics listed here:

• Calculus
• Matrix Theory
• Probability
• Stochastic Processes
• Estimation
• Testing of Hypotheses:
• Non-Parametric Statistics
• Multivariate Analysis
• Regression Analysis

### GATE Exam 2022 Syllabus Statistics

moments, product moments, simple correlation coefficient, joint moment generating function, independence ofrandom variables, functions of random vector and their distributions, distributions of order statistics, joint and marginal distributions of order statistics; multinomial distribution, bivariate normal distribution, samplingdistributions: central, chi-square, central t, and central F distributions.

 TOPICS SUB-TOPICS 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. 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. 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, birthand- 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, coverage probability. Testing of Hypothesis 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.

Any candidate who opts for Statistics as the primary paper will have to select either Mathematics or Physics as their secondary paper. Meanwhile, find the GATE exam pattern 2022 from the details below:

#### GATE Statistics Syllabus Exam Pattern 2022

Candidates are urged to scroll through the GATE Statistics Marking Scheme and other reference material and prepare most efficiently for the Gate Exams 2022. Details of the exam pattern are given below:

• General Aptitude (GA) Marks of Statistics (ST) = 15 Marks
• Subject Marks = 85 Marks
• Total Marks for ST = 100 Marks
• Total Time (in Minutes) = 180 Minutes

## Frequently Asked Questions on GATE Statistics Syllabus 2022

### How many main topics are discussed in the GATE ST Syllabus 2022?

The syllabus constitutes nine main sections. They are Calculus, Matrix Theory, Probability, Stochastic Processes, Estimation, Testing of Hypotheses, Non-Parametric Statistics, Multivariate Analysis and Regression Analysis.

### What are the total marks for GATE Statistics Syllabus?

The GATE statistics amount to 100 marks, 10 Marks from the General Aptitude section and 85 Marks from the subject section.

### What are the sub-topics covered under the “Non-parametric Statistics” section of the GATE Syllabus for Statistics?

The topics covered under the “Non-parametric Statistics” section of the syllabus are 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.