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# isical.ac.in ISI Admission Test JRF Statistics Syllabus : Indian Statistical Institute

Organisation : Indian Statistical Institute
Announcement : Syllabus
Name of Examination : ISI Admission Test
Degree : JRF Junior Research Fellowship
Subject : Statistics

## JRF Statistics Syllabus :

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.

Related : ISI Admission Test LIS & QMS Syllabus Indian Statistical Institute : www.syllabus.gen.in/1232.html

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.

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.