LECTURER IN STATISTICS SYLLABUS

Module 1: Mathematical methods for statistics. 

Classes ^of sets, sigma-algebra, measure, measurabl e functions and properties, Lebesgue measurable set s. Lebesgue integrals and properties. Riemann-Stieltje s' integral. Proper and improper integral, uniform convergence of series and sequences of real numbers /functions. Linear vector space, subspace, independence of vect ors, basis and dimensions. Orthogonal and orthonorm al basis, Gram-Schmidt orthogonalisation , orthogonal transformations. Matrices & determinants-rank, null space, nullity, linear transformations, characteris tic roots & vectors, spectral decomposition, classi fication & reduction of quadratic forms. Generalized inverse a nd properties.

Module II: Probability Theory. 

Probability measure, conditional probability and Ba ye's theorem. Random variable-distribution, density functions and properties. Mathematical expectation and inequalities ( Markov, Chebychev's, Liaponov, Jenson). Different modes of convergence of sequence of random variables, weak and strong law of large numbers. Characteristic functions-elementary proper ties and inverse theorem. Central limit theorems an d its applications.

Module III: Distribution theory 

Basic concepts in distribution theory, generating f unctions ( pgf, mgf, cf). Bivariate distributions-j oint, marginal conditional distributions and expectations . Least square principle, correlation and regressio n. Standard discrete distributions ( Binomial, Poisson , negative binomial, geometric, hyper geometric, po wer series distributions and properties). Continuous di stributions ( Uniform, normal, exponential, double exponential, beta, gamma, Cauchy, Weibull, Pareto, lognormal, logistic distributions, and Pearson's sy stem of distributions. Order statistics-joint, marginal distributions of o rder statistics from uniform and exponential distri butions Sampling distributions- Sample characteristics and their distributions (normal, chi square, t, F)-prop erties and applications.

Module IV: Sampling theory and design of experiments.

 Census and sampling, probability sampling methods ( SRSWR, SRSWOR, systematic, stratified, cluster, multistage samplings). PPS sampling (Des Raj's, Mur thy, Horvitz-Thompson). Ratio and regression method s of estimations and properties. Gauss-Markov set up, basic designs (CRD.RBD.LSD). I ncomplete block designs- BIBID, PBIBD. Factorial experiments ( 2 n and 3 n ) and confounding. Split plot design

Module V: Statistical Inference 

Problem of estimation, Point estimate and interval estimate-basic concepts, general properties of estimates, sufficiency and completeness-exponential family. Fisher's information, C-R inequality, Racf^Blackwell and Lehman-Scheffe theorems. Methods of estimation ( MLE, Moments, Minimum Chi square). Fundamental concepts of testin g of hypotheses. Neyman-Pearson'lemma, most powerful test, UMP test, likelihood-ratio test , large sample and small sample tests. SPRT Non-parametric tests ( Chi square test of goodness fit, K-S test, sign test, Wilcoxon, Signed rank, run, Mann-Whitney, Wilcoxon).

Module VI: Stochastic Processes , Multivariate Analysis 

Definition of stochastic process- basic concepts, M arkov Chain, classification of states, discrete time branching process, Poisson process and related processes. Renewal theorem and limit theorems. Multivariate distributions ( Normal, multinomial)- marginal , conditional and characteristic functions. Distribution of quadratic forms, Partial and multiple correlations. Multivariate sampling distributions^Hotelling's T 2 and Mahalanobis - D 2 . Classification problems- Classifying to one of k mu ltivariate normal populations, discriminant analysis, Principal component analysis, canonical v ariables and canonical correlations.

Module VII Recent developments in Statistics 

Generalized linear modeling. Statistical decision p roblem, Bayesian inference, Prior and posterior distributions, Bayes' estimates, life time distribu tions, basic concepts of survival analysis - surviv al function, hazard rate. Construction and properties; yarious typesjcontrol charts. Acceptance sampling for attributes. Linear programming problem . Markovian Queuing models. Components of time series, ARMA and ARIMA. Basic concepts in Econ ometrics ( demand, revenue, elasticity and equilibrium analysis). Simulation Techniques

Module VIII Research Methodology/Teaching Aptitude 

I. TEACHING APTITUDE
• Teaching: Nature, objectives, characteristics and b asic requirements;
• Learner's characteristics; • Factors affecting teaching;
• Methods of teaching;
• Teaching aids;
• Evaluation systems.
II. RESEARCH APTITUDE
• Research: Meaning, Characteristics and types;
• Steps of research;
• Methods of research;
• Research Ethics;
• Paper, article, workshop, seminar, conference and s ymposium;
• Thesis writing: its characteristics and format.

Module IX(a) Salient Features of Indian Constitution 

Salient features of the Constitution - Preamble- It s significance and its place in the interpretation of the Constitution.
Fundamental Rights - Directive Principles of State Policy - Relation between Fundamental Rights and Directive Principles - Fundamental Duties.
Executive - Legislature - Judiciary - Both at Union and State Level. - Other Constitutional Authorities.
Centre-State Relations - Legislative - Administrati ve and Financial.
 Services under the Union and the States.
Emergency Provisions.
Amendment Provisions of the Constitution.

Module IX (b) Social Welfare Legislations and Programmes 

Social Service Legislations like Right to Informati on Act, Prevention of atrocities against Women & Children, Food Security Act, Environmental Acts e tc. and Social Welfare Programmes like Employment Guarantee Programme, Organ and Blood Don ation etc.

Module X (a) Renaissance in Kerala 

TOWARDS A NEW SOCIETY
Introduction to English education - various mission ary organisations and their functioning- founding of educational institutions, factories, pr inting press etc.
EFFORTS TO REFORM THE SOCIETY 
(A) Socio-Religious reform Movements 
SNDP Yogam, Nair Service Society, Yogakshema Sabha, Sadhu Jana Paripalana Sangham, Vaala Samudaya Parishkarani Sabha, Samathwa Samajam, Isla m Dharma Paripalana Sangham, Prathyaksha Raksha Daiva Sabha, Sahodara Prasthanam etc.
(B) Struggles and Social Revolts 
Upper cloth revolts.Channar agitation, Vaikom Sathy agraha, Guruvayoor Sathyagraha, Paliyam Sathyagraha. Kuttamkulam Sathyagraha, Temple Entry Proclamation, Temple Entry Act .Malyalee Memorial, Ezhava Memorial etc. Malabar riots, Civil Disobedience Movement, Abstent ion movement etc.
ROLE OF PRESS IN RENAISSANCE 
Malayalee, Swadeshabhimani, Vivekodayam, Mithavadi, Swaraj, Malayala Manorama, Bhashaposhini, Mathnubhoomi, Kerala Kaumudi, Samada rsi, Kesari, AI-Ameen, Prabhatham, Yukthivadi, etc
AWAKENING THROUGH LITERATURE 
Novel, Drama, Poetry, Purogamana Sahithya Prasthanam, Nataka Prashtanam, Library movement etc
WOMEN AND SOCIAL CHANGE 
Parvathi Nenmenimangalam, Arya Pallam, A V Kuttimal u Amma, Lalitha Prabhu.Akkamma Cheriyan, Anna Chandi, Lalithambika Antharjanam and others
LEADERS OF RENAISSANCE
Thycaud Ayya Vaikundar, Sree Narayana Guru, Ayyan K ali.Chattampi Swamikal, Brahmananda Sivayogi, Vagbhadananda, Poikayil Yohannan(Kumara G uru) Dr Palpu, Palakkunnath Abraham Malpan, Mampuram Thangal, Sahodaran Ayyappan, Pandi t K P Karuppan, Pampadi John Joseph, Mannathu Padmanabhan, V T Bhattathirippad, Vakkom A bdul Khadar Maulavi, Makthi Thangal, Blessed Elias Kuriakose Chaavra, Barrister G P Pill ai, TK Madhavan, Moorkoth Kumaran, C. Krishnan, K P Kesava Menon, Dr.Ayyathan Gopalan, C V Kunjuraman, Kuroor Neelakantan Namboothiripad, Velukkutty Arayan, K P Vellon, P K Chathan Master, K Kelappan, P. Krishna Pillai, A K Gopalan, T R Krishnaswami Iyer, C Kesav an. Swami Ananda Theerthan , M C Joseph, Kuttippuzha Krishnapillai and others
LITERARY FIGURES 
Kodungallur Kunhikkuttan Thampuran, KeralaVarma Val iyakoyi Thampuran, Kandathil Varghesc Mappila. Kumaran Asan, Vallathol Narayana Menon, Ul loor S Parameswara Iyer, G Sankara Kurup, Changampuzha Krishna Pillai, Chandu Menon, V aikom Muhammad Basheer. Kesav Dev, Thakazhi Sivasankara Pillai, Ponkunnam Varky, S K P ottakkad and others

Module X (b) General Knowledge and Current Affairs 

General Knowledge and Current Affairs

NOTE: - It may be noted that apart from the topics detailed above, questions from other topics prescribed for the educational qualifi cation of the post may also appear in the question paper. There is no undertaking that all the topics above may be covered in the question paper
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