Organisation : Indian Statistical Institute
Announcement : Syllabus
Name Of Exam : ISI Admission Test

Home Page : http://www.isical.ac.in/
Download Syllabus Here : http://www.isical.ac.in/~admission/I...sQuestion.html

ISI Admission Test Syllabus For JRF :
Junior Research Fellowship for Research Course in Statistics :
The candidates for research course in Statistics will have to take two short-answer type tests – STA and STB. Each test is of two-hour duration. Test STA will have about 10 questions of equal value, set from selected topics in Mathematics and Statistics at the undergraduate level. Test STB will have roughly 8 questions of equal value, on topics in Statistics at Master’s level.

Syllabus for STA :
Mathematics Functions and relations. Matrices – determinants, eigenvalues and eigenvectors, solution of linear equations, and quadratic forms. Calculus and Analysis – sequences, series and their convergence and divergence; limits, continuity of functions of one or more variables, differentiation, applications, maxima and minima. Integration, definite integrals, areas using integrals, ordinary linear differential equations. Statistics

(a) Probability : Basic concepts, elementary set theory and sample space, conditional probability and Bayes theorem. Standard univariate and multivariate distributions. Transformations of variables. Moment generating functions, characteristic functions, convergence in probability, first and second Borel-Cantelli lemmas, almost sure convergence, weak and strong laws of large numbers, convergence in distribution and central limit theorem. Markov chains.

(b) Inference : Sufficiency, minimum variance unbiased estimation, Bayes estimates, maximum likelihood and other common methods of estimation. Optimum tests for simple and composite hypotheses. Elements of sequential and non-parametric tests. Analysis of discrete data – contingency chi-square.

(c) Multivariate Analysis : Standard sampling distributions. Order statistics with applications. Regression, partial and multiple correlations. Basic properties of multivariate normal distribution, Wishart distribution, Hotelling’s T2 and related tests.

(d) Design of Experiments : Inference in linear models. Standard orthogonal and non-orthogonal designs. Analysis of general block designs. Factorial experiments. One and two-way ANOVA.

(e) Sample Surveys : Simple random sampling, Systematic sampling, PPS sampling, Stratified sampling. Ratio and regression methods of estimation. Non-sampling errors, Non-response bias.

Test Codes: UGA (Multiple-choice Type) and UGB (Short Answer Type) 2017
Questions will be set on the following and related topics.

Algebra: Sets, operations on sets. Prime numbers, factorization of integers and divisibility. Rational and irrational numbers. Permutations and combinations, basic probability. Binomial Theorem. Logarithms.

Polynomials : Remainder Theorem, Theory of quadratic equations and expressions, relations between roots and coefficients. Arithmetic and geometric progressions. Inequalities involving arithmetic, geometric & harmonic means. Complex numbers. Matrices and determinants.

Geometry : Plane geometry. Geometry of 2 dimensions with Cartesian and polar coordinates. Equation of a line, angle between two lines, distance from a point to a line. Concept of a Locus. Area of a triangle. Equations of circle, parabola, ellipse and hyperbola and equations of their tangents and normals. Mensuration.

Trigonometry : Measures of angles. Trigonometric and inverse trigonometric functions. Trigonometric identities including addition formulae, solutions of trigonometric equations. Properties of triangles. Heights and distances.

Calculus : Sequences - bounded sequences, monotone sequences, limit of a sequence. Functions, one-one functions, onto functions. Limits and continuity. Derivatives and methods of differentiation. Slope of a curve. Tangents and normals.

Maxima and minima. Using calculus to sketch graphs of functions. Methods of integration, definite and indefinite integrals, evaluation of area using integrals.