INDIAN STATISTICAL INSTITUTE

**Course Name : **M.Stat**Duration : **2 year**Venue : **Kolkata, Delhi, Chennia, Bangalore**Stipend : **Rs.5000/month (Revised)**Contigency/Book Grant : **Rs.5000/year (Revised)**Scope : **This two-year programme offers advanced-level training in the theory, methods and applications of Statistics along with specialised training in selected areas of Statistics and allied fields. On successful completion of this programme, students will be able to pursue an academic/ research career in Statistics, Mathematics, Economics, Computer Science and allied fields, depending on their chosen area of specialisation. They will also be able to work competently as Statisticians and research institutions and scientific laboratories, government departments or industries .This programme is being offered at any two centres out of four.

**Eligibility : **

In order to be eligible for admission to the M.Stat. Programme, a student must have

A 3- year Bachelor’s degree with Statistics as full subject, or

A B.Stat./B.Math. degree from the Indian Statistical Institute.

A Statistician’s Diploma/Senior Diploma/Post-graduate diploma in Statistical methods with Applications from Indian Statistical Institute.

**Examination Pattern & Selection Procedure**

Students with B.Stat.(Hons.) degree from Indian Statistical Institute are offered direct admission to the M.Stat. programme without any selection test and interview. For all other eligible candidates, including students with B.Stat.(Pass) degree from Indian Statistical Institute, selection for admission to the M.Stat. programme is based on performance in written selection tests and subsequent interview. Past academic record may also be taken into consideration.

**The written selection tests consist of : **

A test comprising multiple-choice and/or short-answer questions in Mathematics at Bachelor’s degree level, and a test comprising multiple-choice and/or short-answer questions in Statistics and Mathematics at a three-year Bachelor’s degree level, designed to assess competence in the theory and methods of Statistics and comprehension in Mathematics.

**Notification Date : **2nd week of February**Exam Date : **May 2nd week

**Sample Questions are also available on website **www.isical.ac.in

**SYLLABUS for Entrance ExamTEST CODE : MMA (Objective type)Analytical ReasoningAlgebra – **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. Eigen values 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. Differentiation and integration of functions of one variable with applications. Definite integrals. Maxima and minima. Functions of several variables-limits, continuity, differentiability. Double integrals and their applications. Ordinary linear differential equations.

Elementary discrete probability theory – combinatorial probability, conditional probability, Bayes theorem. Binomial and Poison distributions.

**Test Code PSB MS(Stat) (Short answer type)Syllabus for MathematicsCombinatorics : **

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 ProbabilityProbability 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 and methods of estimation (unbiased ness, 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 non-parametric 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.

**Placement of Students**

Students who have undergone the M.Stat. and other degree, diploma/certificate courses of the Institute and those having the Ph.D. degree of the Institute are now well-placed in government and semi-government departments, public and private sector undertakings, industries and research/educational institutions, both in India and abroad. Most of the students of the Institute get employment offers or admission to some Ph.D. programmes even before they complete the qualifying degree examinations.

*** There is a Placement Committee in Kolkata, which arranges campus interviews by prospective employers.**

* Campus interviews are also organized at ISI Delhi and Bangalore Centers.

* Campus interviews are also organized at ISI Delhi and Bangalore Centers.