GATE Syllabus

GATE 2021 syllabus – Statistics

GATE 2021 syllabus for Statistics gives you details of the latest GATE syllabus for the subject release by the official gate organizing institute. We also created an easy to use ad-free mobile app for GATE syllabus, previous year papers with keys, gate calculator, virtual calculator, and more. Download for iStudy for all GATE preparation needs.

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GATE syllabus for Statistics (ST)

General Aptitude (Common To All Papers)

Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.

Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data interpretation.

General Aptitude Sample Questions

Verbal Ability

Choose the appropriate answer to complete the following sentence:

To those of us who had always thought him timid, his _________________came as a surprise.

(A) intrepidity

(B) inevitability

(C) inability

(D) inertness

Choose the appropriate answer to complete the following sentence:

Medicine is to illness as law is to____

(A) discipline

(B) anarchy

(C) treason

(D) etiquette

Read the following paragraph:

The ordinary form of mercury thermometer is used for temperature ranging from -40 degree fahrenheit to 500 degree fahrenheit. For measuring temperature below -40 degree fahrenheit, thermometers filled with alcohol are used. These are, however, not satisfactory for use in high temperatures. When a mercury thermometer is used for temperature above 500 degree fahrenheit, the space above the mercury is filled with some inert gas, usually nitrogen or carbon dioxide, placed in the thermometer under pressure. As the mercury rises, the gas pressures is increased, so that it is possible to use these thermometers for temperatures as high as 1000 degree fahrenheit.

With what, besides mercury, would a thermometer be filled if it was designed to be used for measuring temperature of about 500 degree fahrenheit?

(A) Pyrometer

(B) Inert gas

(C) Iron and brass

(D) Gas

The cost of manufacturing tractors in Korea is twenty percent less than the cost of manufacturing tractors in Germany. Even after transportation fees and import taxes are added, it is still cheaper to import tractors from Korea to Germany than to produce tractors in Germany.

Which of the following assertions is best supported by the above information?

(A) Labour costs in Korea are twenty percent below those in Germany.

(B) Importing tractors into Germany will eliminate twenty percent of the manufacturing jobs in Germany.

(C) The costs of transporting a tractor from Korea to Germany is more than twenty percent of the cost of manufacturing the tractor in Korea.

(D) The import taxes on a tractor imported from Korea to Germany is less than twenty percent of the cost of manufacturing the tractor in Germany.

Numerical Ability

In a survey, 3/16 of the people surveyed told that they preferred to use public transport while commuting daily to office. 5/8 of the people surveyed told that they preferred to use their own vehicles. The remaining 75 respondents said that they had no clear preference. How many people preferred to use public transport?

(A) 75

(B) 100

(C) 125

(D) 133

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.

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 ordermoments.

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-deathprocesses.

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 correlationcoefficients.

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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