GATE 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 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, skewHermitian, 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, MannWhitney 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; Hotellings 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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