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Instruction for even semester of 2017-18 Ph.D. written test

This for the students who have applied for the PhD position for even semester of 2017-18 academic year. The details of the PhD written test is the following:

 

The Ph.D. admission test is for 100 marks, out of which written test is for 45 marks and interview is for 55 marks. The questions for the written test shall be of multiple choice type (more than one option may also be correct) and/or fill in the blank type and the exam duration will be for two hours. There will be 15 questions, each of 3 marks, from each of the following two groups, namely  1. Probability, 2. Statistics.

 

A student will choose one group and needs to answer the 15 questions corresponding to that group. Depending on the number of students appearing in the written test, a cut off mark may be decided by the committee to shortlist the candidates to appear in the interview.

 

Syllabus for Written Test

Probability:

Series and sequences, Continuous and differentiable functions, Mean value theorem, Maxima and minima, Riemann integration. Sequence and series of functions, Uniform convergence, Space of continuous functions C[0; 1].

 

Lebesgue measure, Measurable functions, Lebesgue integral, Basic properties of Lebesgue integral, Differentiation and Lebesgue measure, LSpaces, Holder and Minkowski inequalities, convergence in measure, Monotone and Dominated convergence theorems, Fatou’s lemma.

 

Combinatorial probability and urn models; Conditional probability and independence; Random variables discrete and continuous; Expectations, variance and moments of random variables; Probability inequalities; Transformations of univariate random variables; Jointly distributed random variables; Conditional expectation; Generating functions; Limit theorems.

 

Statistics:

 

 

Standard univariate and multivariate distributions, Multivariate normal distribution, Types of convergence of random variables, Descriptive statistical measures, Standard sampling distributions, Order statistics, Theory of point estimation: unbiasedness, consistency, sufficiency, minimum variance unbiased estimation, Methods of estimation: method of moments, maximum likelihood estimation and its properties, Bayes estimation, Confidence set estimation, Bayesian intervals, Tests of hypothesis: uniformly most powerful tests for simple and composite hypotheses, p-value, Likelihood ratio tests, Large sample tests, Correlation, Multiple linear regression and related inference, Logistic regression, Analysis of variance, Standard Nonparametric tests.

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School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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