Syllabus for M. Stat Entrance Exam

I want to take admission in M. Stat at ISI so please give me syllabus for preparation of entrance exam and other important details?

[Kiran Chandar]

M. Stat at ISI (Indian Statistical Institute) is study of theory, methods and applications of Statistics along with specialized training in selected areas of Statistics and allied fields.

Students would be able to pursue an academic/research career in Statistics, Mathematics, Economics, Computer Science and allied fields or for in research institutions and scientific laboratories, government departments or industries.

Eligibility:
B. Sc, or a B. E. / B. Tech. with Mathematics with an exceptionally strong background in Analysis and Abstract Algebra.

Entrance Exam Syllabus:

Analytical Reasoning:

Algebra | Arithmetic, geometric and harmonic progression. Continued fractions. Elementary combinatorics: Permutations and combinations, Binomial theorem. Theory of equations. Inequalities. Complex numbers and De Moivre's theorem. Elementary set theory. Functions and relations.
Elementary number theory:
Divisibility, Congruences, Primality. Algebra of matrices. Determinant, rank and
inverse of a matrix. Solutions of linear equations. Eigenvalues and eigenvectors of
matrices. Simple properties of a group.
Coordinate geometry | Straight lines, circles, parabolas, ellipses and hyperbolas.

Calculus | Sequences and series:
Power series, Taylor and Maclaurin series.
Limits and continuity of functions of one variable. Di erentiation and integration of
functions of one variable with applications. De nite integrals. Maxima and minima.
Functions of several variables - limits, continuity, di erentiability. Double integral
and their applications. Ordinary linear di erential equations.
Elementary discrete probability theory | Combinatorial probability, Conditional probability, Bayes theorem. Binomial and Poisson distributions.


Mathematics:

Combinatorics; Elements of set theory. Permutations and combinations.
Binomial and multinomial theorem. Theory of equations. Inequalities.

Linear Algebra
Vectors and vector spaces. Matrices. Determinants. Solution of linear equations
Trigonometry. Co-ordinate geometry.

Complex Numbers
Geometry of complex numbers and De Moivres theorem.

Calculus
Convergence of sequences and series. Functions. Limits and continuity of functions of one or more variables. Power series. Diferentiation.
Leibnitz formula. Applications of diferential calculus, maxima and minima.
Taylor’s theorem. Diferentiation of functions of several variables. Indefinite integral. Fundamental theorem of calculus. Riemann integration and properties. Improper integrals. Double and multiple integrals and applications.


Statistics and Probability:

Probability and Sampling Distributions
Notions of sample space and probability. Combinatorial probability. Conditional probability and independence. Random variables and expectations. Moments and moment generating functions. Standard univariate discrete and continuous distributions. Joint probability distributions. Multinomial distribution. Bivariate normal and multivariate normal distributions. Sampling distributions of statistics. Weak law of large numbers. Central limit theorem.

Descriptive Statistics
Descriptive statistical measures. Contingency tables and measures of association. Product moment and other types of correlation. Partial and multiple correlation. Simple and multiple linear regression.

Statistical Inference
Elementary theory of estimation (unbiasedness, minimum variance, sufciency). Methods of estimation (maximum likelihood method, method of moments). Tests of hypotheses (basic concepts and simple applications of Neyman-Pearson Lemma). Confidence intervals. Inference related to regression. ANOVA. Elements of nonparametric inference.

Design of Experiments and Sample Surveys
Basic designs such as CRD, RBD, LSD and their analyses. Elements of factorial designs. Conventional sampling techniques (SRSWR/SRSWOR) including stratification. Ratio and regression methods of estimation.








Here I am providing you some previous years question papers of M. Stat entrance exam at ISI.



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