ISI M.STAT Entrance Exam Syllabus

Syllabus of ISI  M.STAT Entrance Exam
MMA Paper
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 integrals
and their applications. Ordinary linear di erential equations.
Elementary discrete probability theory | Combinatorial probability, Conditional probability, Bayes theorem. Binomial and Poisson distributions.

Test Code PSB (Short answer type)Syllabus for 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. Differentiation.
Leibnitz formula. Applications of differential calculus, maxima and minima.
Taylor’s theorem. Differentiation of functions of several variables. Indefinite
integral. Fundamental theorem of calculus. Riemann integration and properties. Improper integrals. Double and multiple integrals and applications.
Syllabus for 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, sufficiency). 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.