# GATE 2021 Statistics Syllabus (Released) – Get (ST) PDF Here

** GATE 2021 Syllabus of Statistics** has been Released**.** **GATE 2021** is a national level exam organized by **IIT Delhi**.

The Engineering Graduation Skill Test (**GATE 2021**) is organized for admission to PG courses in the field of engineering and technology, specifically ME / M.Tech.

The** Exam **will be** held **on 1st week of **February 2021. **See here for complete information about the **GATE 2021 Syllabus**.

## GATE 2021 Statistics Syllabus – PDF Released

** GATE 2021 Statistics Syllabus has been Released. Click Here to Download PDF.**

## GATE 2021 Statistics Syllabus

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* 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, a 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.

* 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, 22 and 23 Factorial Experiments.

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* Linear Algebra: *Matrices and Determinants, Systems of linear equations, Eigenvalues and eigenvectors.

* Calculus:* Limit, continuity, and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.

* Vector Calculus:* Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green’s theorems.

* Differential Equations:* Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs -Laplace, heat and wave equations.

* Probability and Statistics:* Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.

* Numerical Methods: *Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.

If you any query regarding** GATE 2021 Statistics Syllabus,** you can ask your query leave comments below.