INDIAN INSTITUTE OF TECHONOLOGY (RANK 1)

From the Academic Session 2004-05, Indian Institutes of Technology have started conducting a Joint Admission Test for M.Sc. (JAM). The objective of JAM is to provide admissions to M.Sc. (Two Year), Joint M.Sc.-Ph.D., M.Sc.- Ph.D. Dual Degree and other Post-Bachelor’s Degree programmes at the IITs and to the Integrated Ph.D. programmes at IISc and to consolidate Science as a career option for bright students from across the country. JAM is expected to serve as a benchmark for undergraduate level science education in the country. IISc is joining the JAM for the first time this year to select candidates to its Integrated Ph.D. Programmes. The integrated Ph.D. Programmes at IISc was started in the early 90’s to enable students to directly join for a Ph.D. degree after their B.Sc. Degree.

The M.Sc. (Two Year), Joint M.Sc.-Ph.D, M.Sc.-Ph.D. Dual Degree and other post-bachelor’s degree programmes at the IITs and the integrated Ph.D. programmes at IISc offer high quality education in their respective disciplines, comparable to the best in the world. The curricula for these programmes are designed to provide the students with opportunities to develop academic talent leading to challenging and rewarding professional life. The curricula are regularly updated at IISc, Bangalore & IITs. The interdisciplinary content of the curricula equips the students with the ability to utilize scientific knowledge for practical applications. The medium of instruction in all the programmes is English.

#### JOINT ADMISSION TEST FOR M.Sc.

**Name of the Course/s : **

1. IIT Bombay (IITB): Two-year Master of Science (M.Sc.) programs in: Applied Statistics and Informatics. (37) 19+10+5+3

2. IIT Kanpur (IITK): Two-year Master of Science (M.Sc.) programs in: Statistics. (40 seats) 20+11+6+3

3. IIT Delhi (IITB): Two- year M.Sc.- Ph.D. Dual Degree in O.R.(12 seats) 6+3+2+1**Eligibility : **The candidates who qualify in JAM 2012 shall have to fulfill the following eligibility criteria for admissions in IITs.**(i)** At least 55% aggregate marks (taking into account all subjects, including languages and subsidiaries, all years combined) for General/OBC category candidates and at least 50% aggregate marks (taking into account all subjects, including languages and subsidiaries, all years combined) for SC, ST and PD category candidates in the qualifying degree.

For candidates with letter grades/CGPA (instead of percentage of marks), the equivalence in percentage of marks will be decided by the Admitting Institute(s).**(ii)** Proof of having passed the qualifying degree with the minimum educational qualification as specified by the admitting institute should be submitted by 30 September of the academic year.

At the time of admission, all admitted candidates will have to submit a physical fitness certificate from a registered medical practitioner in the prescribed form. At the time of registration, the admitted candidates may also have to undergo a physical fitness test by a medical board constituted by the Admitting Institute. In case a candidate is not found physically fit to pursue his/her chosen course of study, his/her admission is liable to be cancelled.**Examination Pattern : **Test paper will be objective-cum-descriptive type. There will be a “question-cum-answer booklet” for this paper. Answers to various questions are to be given at appropriate places in the “question-cumanswer booklet” itself. No supplementary sheet will be provided. Test duration is 3 hours and maximum marks 100.The test paper will have** multiple choice type questions(MCQ) and descriptive type questions,** carrying weightages of 60% and 40%, respectively. The objective type questions in these test paper will have four choices as possible answers, of which, only one will be correct. There will be negative marking for wrong answers to the objective type questions. Each objective type question carries 3 marks for a correct answer and negative 0.50 marks for a wrong answer. There will be no negative marking for descriptive type questions. Use of calculator (non programmable) is permitted.**Notification Date : **2nd week of September**Exam date : **2nd week of February**SYLLABUS FOR MATHEMATICAL STATISTICS (MS) TEST PAPER**

The Mathematical Statistics (MS) test paper comprises of Mathematics (40% weightage) and Statistics (60% weightage).**Mathematics Syllabus****Sequences and Series : **Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.**Differential Calculus : **Limits, continuity and differentiability of functions of one and two variables. Rolle’s theorem, mean value theorems, Taylor’s theorem, indeterminate forms, maxima and minima of functions of one and two variables.**Integral Calculus : **Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes.**Matrices : **Rank, inverse of a matrix. systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices.**Differential Equations : **Ordinary differential equations of the first order of the form y’ = f(x,y). Linear differential equations of the second order with constant coefficients.**STATISTICS Syllabus****Probability : **Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes’ theorem and independence of events.**Random Variables : **Probability mass function, probability density function and cumulative distribution functions, distribution of a function of a random variable. Mathematical expectation, moments and moment generating function. Chebyshev’s inequality.**Standard Distributions : **Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution.**Joint Distributions :**Joint, marginal and conditional distributions. Distribution of functions of random variables. Product moments, correlation, simple linear regression. Independence of random variables.**Sampling distributions : **Chi-square, t and F distributions, and their properties.**Limit Theorems : **Weak law of large numbers. Central limit theorem (i.i.d.with finite variance case only).**Estimation : **Unbiasedness, consistency and efficiency of estimators, method of moments and method of maximum likelihood. Sufficiency, factorization theorem. Completeness, Rao-Blackwell and Lehmann-Scheffe theorems, uniformly minimum variance unbiased estimators. Rao-Cramer inequality. Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions.**Testing of Hypotheses : **Basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of univariate normal distribution.**More information is available on : ****Indian Institute of Technology Bombay****Indian Institute of Technology Delhi****Indian Institute of Technology Guwahati****Indian Institute of Technology Kanpur****Indian Institute of Technology Kharagpur****Indian Institute of Technology Madras****Indian Institute of Technology**