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# GATE Syllabus 2020 for Statistics – GATE Exam Syllabus

## GATE Exam Syllabus 2020 for Statistics

GATE Statistics Syllabus: Here we bring you the Gate 2020 Exam Syllabus for Statistics subject to prepare for the Graduate Aptitude Test in Engineering (GATE), an all India level examination conducted by the GATE Committee. Check out the GATE Syllabus for Statistics and other important aspects of the GATE Exam Statistics Syllabus.

### GATE Statistics 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 the 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.

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 existence of higher order moments.

Stochastic Processes: 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.

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 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, 22 and 23 Factorial experiments.

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