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## GATE(ST) SYLLABUS

IIT GATE Syllabus for Statistics (MS)

The GATE test paper for Statistics consists of two subjects which are Mathematics and Statistics. Aspirants can go through the detailed GATE(ST) Statistics syllabus here. Find out the important topics for the Statistics course below:

GATE Mathematics Syllabus

• Calculus: 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.

• Linear Algebra: 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.

GATE Statistics Syllabus

• Probability: 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 the existence of higher-order moments.

• Stochastic Processes: Markov chains with finite and countable state space, classification of states, limiting behavior of n-step transition probabilities, stationary distribution, Poisson, and birth-and-death processes.

• Inference: 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.

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

• Multivariate Analysis: Basic properties of the multivariate normal distribution; Multinomial distribution; Wishart distribution; Hotelling’s T2 and related tests; Principal component analysis; Discriminant analysis; Clustering.

• Design of Experiments: One and two-way ANOVA, CRD, RBD, LSD, 2^2, and 2^3 Factorial experiments.

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