# GATE 2022 – IIT Kharagpur

In this article we are sharing the syllabus of GATE 2022 Statistics syllabus by IIT Kharagpur. All Statistics branch candidates who want to appear in GATE 2022 with GATE 2022 Paper Code ‘ST’ must download this syllabus before starting preparation.

## IIT Kharagpur : GATE 2022 Syllabus – Statistics (ST)

GATE 2022 will be conducted by IIT Kharagpur. IIT Kharagpur tentative syllabus and paper pattern for GATE 2022 Statistics is available in this post. Kindly read full article, download the GATE 2022 syllabus PDF and share this article with your friends.

Paper Sections Marks Distribution
General Aptitude 15% Of Maximum Marks
Subject Question 85% Of Maximum Marks
Total 100% 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, method of Lagrange’s multipliers; Double and Triple integrals and their applications; Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.

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.

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 existence of higher order moments.

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.

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.

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

Basic properties of multivariate normal distribution; Multinomial distribution; Wishart distribution; Hotellings T2 and related tests; Principal component analysis; Discriminant analysis; Clustering.

One and two-way ANOVA, CRD, RBD, LSD, 22 and 23 Factorial experiments.