UNIVERSITY OF DELHI (RANK 1)

The Department of Mathematical Statistics was established in August 1973, though the teaching of M.A. in Mathematical Statistics had been introduced as early as in July 1957 at the initiative of Professor Ram Behari as part of a development programme adopted by the Department of Mathematics. Professor H.C. Gupta was the first head of the Department and he can be credited with the setting up of a good school in Stochastic Processes. In 1987, the Department of Mathematical Statistics was re-named as the Department of Statistics. The Department is running the post-graduate (M.A./M.Sc.), M.Phil. and Ph.D. Programmes in Statistics. In 1971, the scope of post-graduate course in Mathematical Statistics was extended leading to M.Sc. degree in Mathematical Statistics.

The syllabus of M.A./ M.Sc. course has been revised and restructured periodically to incorporate and reflect the latest in the discipline. The Department imparts rigorous training and exposure to the students in computer education by way of introducing the latest state-of-the-art in the programming language and computer software to enable the students to perform statistical data analysis. With a view to preparing research background of the students, the M. Phil. course in Mathematical Statistics was introduced in 1977 and the same has been continually updated covering most of the topical areas of Theoretical and Applied Statistics at the specialization level.

The Department has laboratories equipped with the basic and modern computing facilities. There is a good collection of books in laboratories with latest titles in various areas of statistics. Two computer laboratories with latest computing systems and related equipment have been setup in the Department for the use of students, research scholars and teachers. Regarding the job opportunities for the alumni, the Department has its own placement cell operating since academic year 2005-06. We can take pride in the fact that students get suitable placement in Research Institutes or Industries or Government Departments. Quite a few are selected in Indian Statistical Service (ISS) each year.

**COURSE OF STUDY IN STATISTICS Sl.No. Course No.of seats**

1. M.A./M.Sc. Statistics 93 (North & South Delhi Campus) Gen-47, SC-14, ST-07, OBC-25

*Supernumerary Seats : PWD-03, Sports/ECA-05, Foreign Students-05

**Duration of the Course : **Two years ( 4 – Semisters )**IMPORTANT DATES**

Online Registration start : 2nd week of March

Date of Entrance Examination : 3rd week of june

Timings : 0:00a.m. to 1:00 p.m.

Date of declaration of result of Entrance Test : 2nd week of July (Tentative>

Date of Admission List : 3rd week of July (Tentative)**4 . ADMISSION PROCEDURE AND ELIGIBLITY CONDITIONS FOR ADMISSION TO M.A./M.Sc. COURSE IN STATISTICS 2014-2015 **

Admission to Post-Graduate Course in Statistics leading to a Master’s Degree in Statistics will be made through two modes:

Mode-I : Direct Admission ( only for Delhi students)

Mode-II : Through an Entrance Test**Mode-II : **The remaining 50% seats will be filled on the basis of merit in an entrance examination from the candidates satisfying any of the following eligibility criteria:

Any candidate who has obtained bachelor’s degree in any subject and has studied at least 3 courses each of one year duration or 6 courses each of one semester duration in Statistics under 10+2+3 scheme of examination securing at least 50% marks in aggregate will be eligible to appear in entrance examination.

Any candidate who has obtained bachelor’s degree in Mathematics (Hons.) or Computer Science (Hons.) with at least one paper in Statistics under 10+2+3 scheme of examination of the University of Delhi or any other examination recognized as equivalent thereto with at least 50% marks in aggregate and at least 60% marks in a paper of Statistics. Any candidate appearing in the final year examination of bachelor’s degree of the same calendar year shall also be eligible to appear in the entrance test, however, he/she will be considered for admission if he/she fulfills the other requirements of admission.

**Number of Seats Available : Mode-II : 93**

General Category : 23

SC Category : 07

ST Category : 04

OBC : **Modalities :**

- The candidates belonging to reserved categories will be provided relaxations/ reservations as per University rules in both the Modes of admission. It may be noted that candidates can apply simultaneously under GEN/SC/ST/OBC/PwD/Sports/ECA/CW categories.
- Under Mode-II the minimum requirement for candidates belonging to SC/ST categories will be 40% marks in aggregate and for OBC category will be 45% marks in aggregate.
- The entrance examination shall be of three hours duration. The question paper shall be of 400 marks consisting of 100 MCQs (multiple choice questions).
- Each MCQ carries 4 marks. For each correct response the candidate will get 4 marks.

For each incorrect response shown in the answer-sheet, one mark will be deducted. No mark will, however, be deducted for not attempting a question. More than one response indicated against a question in the answer-sheet will be considered as incorrect response and will be negatively marked. **Entrance Examination fee : **

The GEN/OBC category candidates applying for admission to M.A./M.Sc. (Part-I) Statistics course shall be charged registration fee @ Rs.500/- for each application. In the case of candidates belonging to SC/ST/PWD category, the registration fee will be Rs.250/- for each application payable by a bank draft drawn in favour of the **Registrar, University of Delhi, Delhi-110007 payable at Delhi or by on-line gateway payment **as per the final decision of the University authorities in this matter. **Syllabus for the Entrance Test Linear Algebra : **Elements of set theory. Vector space, subspace and its properties. Linear independence and dependence of vectors. Matrices, rank of a matrix, reduction to normal forms, linear homogeneous and non-homogeneous equations. Cayley-Hamilton theorem, characteristic roots and vectors. De Moivre’s theorem, relation between roots and coefficient of n

^{th}degree equation. Solution to cubic and biquadratic equation.

**Calculus :**Limit and continuity, differentiability of functions, successive differentiation. Leibnitz’s theorem, partial differentiation. Euler’s theorem on homogeneous functions. Tangents and normals, asymptotes, singular points, curve tracing, reduction formulae. Integration and properties of definite integrals, quadrature. Rectification of curves. Volumes and surfaces of solids of revolution.

**Differential Equations :**Linear, homogeneous, separable equations. First order higher degree equations, algebraic properties of solutions. Linear homogeneous equations with constant coefficients. Solution of second order differential equations.

**Probability and Sampling Distributions :**Notions of sample space and probability. Theorems on probability. Combinatorial probability. Conditional probability and independence. Bayes theorem and its applications. Random variables and expectations. Moments and moment generating functions. Cumulants and Cumulant generating functions. Characteristic function. Standard univariate discrete and continuous distributions. Bivariate probability distributions. Marginal and Conditional distributions. Independence of variates. Bivariate normal and multivariate normal distributions. Transformation in univariate and bivariate distributions. Chebychev’s inequality. Weak law of large numbers. Strong law of large numbers. Central limit theorem. Sampling distribution of a statistic, standard errors of sample mean and sample proportion. Sampling distribution of sample mean and sample variance for normal distribution. Sampling distributions of Chi-square, t- and F- statistics.

**Descriptive Statistics :**Measures of location and dispersion. Measures of skewness and kurtosis. Absolute moments and factorial moments. Inequalities concerning moments. Theory of attributes, consistency of data, conditions for consistency, independence and association of attributes, measures of association and contingency. Correlation and regression. Karl Pearson’s coefficient of correlation. Lines of regression. Rank correlation. Intraclass correlation. Multiple and partial correlations. Simple linear regression.

**Statistical Inference :**Elementary theory of estimation (consistency, unbiasedness, minimum variance, sufficiency). Minimum variance unbiased estimators. Cramer-Rao inequality. Methods of estimation (maximum likelihood method, method of moments). Rao-Blackwell and Lehmann-Scheffe theorems. Interval estimation (confidence intervals for the parameters of normal distribution, confidence intervals for difference of means and for ratio of variances). Tests of hypotheses (basic concepts, MP test and region, simple applications of Neyman-Pearson lemma, likelihood ratio test, UMP test, UMPU test). Non-parametric tests (sign-test, Wald-Wolfowitz run test, run test for randomness, median test, Wilcoxon-Mann-Whitney test).

**Sample Surveys and Design of Experiments :**Sampling and non-sampling errors. Conventional sampling techniques (SRSWR/SRSWOR, stratified random sampling, systematic sampling). Ratio and regression methods of estimation.

ANOVA and ANOCOVA. Basic designs such as CRD, RBD, LSD and their analyses. Missing plot technique. 2

^{n}(n≥5)Factorial experiments and their construction and analysis. Total and partial confounding.

**FOR M.A./M.Sc. COURSE IN STATISTICS**

Admission for mode-II shall be made on the basis of merit in the Entrance Examination to be held on 3rd week of June 2015 and in order of preference given by the candidate and upto the number of seats available in the Colleges.

**SCHOLARSHIPS UNDER ORDINANCE XXVIII**

(i) POST-GRADUATE SCHOLARSHIP (ALL INDIA SCHEME)

(i) POST-GRADUATE SCHOLARSHIP (ALL INDIA SCHEME)

Post-Graduate Scholarships not exceeding twenty in number each of the value of Rs. 250/- p.m., will be awarded each year in the Faculties of Arts, Science, Mathematical Sciences, Social Science, Law, Music and Fine Arts, Management Studies for proceeding to the Degree of M.A./M.Sc./M.Com./ M.B.A./L.L.B./L.L.M. of the University.

**(ii) SANJEEV KUMAR SINGHAL MEMORIAL SCHOLARSHIPS**

There shall be two Scholarships, known as Sanjeev Kumar singhal Memorial Scholarships, to be awarded, each year to the M.A./M.Sc. Statistics students of this University out of the annual income accruing from the Endowment Fund of Rs. 50,000/- (Fifty thousand only) given by his father Dr. Kanwar Sen, Former Professor, Department of Statistics, Faculty of Mathematical Sciences, University of Delhi, Delhi. Value of the Scholarship: Rs.250/- per month each.

**INFORMATION ABOUT RESIDENTIAL ACCOMMODATION**

The University has limited residential accommodation in Colleges and University Hostels. The College provides accommodation to both undergraduate and postgraduate students enrolled in the College.