Saturday 7 January 2017

KERALA PSC HIGHER SECONDARY SCHOOL TEACHER STATISTICS (CATEGORY NO. 356/16) HIGHER SECONDARY EDUCATION

KERALA PSC HIGHER SECONDARY SCHOOL TEACHER STATISTICS (CATEGORY NO. 356/16) -VHSE
Name of the DepartmentKerala Higher Secondary Education
Exam Date: 13/03/2017 Monday

Time: 10.00 AM to 12.15 PM

Module 1: Mathematical methods for statistics.
Classes ^of sets, sigma-algebra, measure, measurable functions and properties, Lebesgue measurable sets. Lebesgue  integrals  and  properties.  Riemann-Stieltjes'  integral.  Proper  and  improper  integral,  uniform convergence of series and sequences of real numbers/functions.
Linear vector space, subspace, independence of vectors, basis and dimensions. Orthogonal and orthonormal basis,  Gram-Schmidt orthogonalisation ,  orthogonal  transformations.  Matrices  & determinants-rank, null space, nullity, linear transformations, characteristic roots & vectors, spectral decomposition, classification & reduction of quadratic forms. Generalized inverse and properties.

Module II: Probability Theory.
Probability  measure,  conditional  probability and  Baye'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 properties and inverse theorem. Central limit theorems and its applications.

Module III: Distribution theory
Basic  concepts  in distribution theory,  generating functions (  pgf,  mgf,  cf).  Bivariate  distributions-joint, marginal conditional distributions and expectations. Least square principle, correlation and regression.
Standard discrete distributions ( Binomial, Poisson, negative binomial, geometric, hyper geometric, power series  distributions  and  properties).  Continuous  distributions  (  Uniform,  normal,  exponential,  double exponential, beta, gamma, Cauchy, Weibull, Pareto, lognormal, logistic distributions, and Pearson's system of distributions.
Order statistics-joint, marginal distributions of order statistics from uniform and exponential distributions
Sampling distributions- Sample characteristics and their distributions (normal,  chi square,  t,  F)-properties 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, Murthy, Horvitz-Thompson). Ratio and regression methods of estimations and properties.
Gauss-Markov set up, basic designs (CRD.RBD.LSD). Incomplete block designs- BIBID, PBIBD. Factorial experiments ( 2n and 3n) 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 testing 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,  Markov 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 T2 and Mahalanobis - D2.
Classification problems-  Classifying to one of  k multivariate  normal  populations,  discriminant analysis, Principal component analysis, canonical variables and canonical correlations.

Module VII Recent developments in Statistics 
Generalized linear modeling. Statistical decision problem, Bayesian inference, Prior and posterior distributions, Bayes' estimates, life time distributions, basic concepts of survival analysis - survival 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 Econometrics ( demand, revenue, elasticity and equilibrium analysis). Simulation Techniques.

Module VIII
RESEARCH METHODOLOGY/TEACHING APTITUDE

I. TEACHING   APTITUDE
• Teaching: Nature, objectives, characteristics and basic 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 symposium;
• Thesis writing: its characteristics and format.

Part IX(a) Salient Features of Indian Constitution 
Salient features of the Constitution - Preamble- Its 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 - Administrative and Financial.
Services under the Union and the States. Emergency Provisions.
Amendment Provisions of the Constitution.

Part 1X(b)Social Welfare Legislations and Programmes
Social  Service Legislations  like Right  to Information Act,  Prevention of  atrocities against Women & Children, Food Security Act, Environmental Acts etc. and Social Welfare Programmes like Employment  Guarantee Programme,  Organ and Blood Donation
etc.

Part X(a) Renaissance in Kerala

TOWARDS A NEW SOCIETY
Introduction to English education - various missionary organisations and their functioning- founding
of educational institutions, factories.printing 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, Islam Dharma Paripalana Sangham, Prathyaksha Raksha Daiva Sabha, Sahodara Prasthanam etc.

(B) Struggles and Social Revolts
Upper  cloth  revolts.Channar  agitation,  Vaikom  Sathyagraha,  Guruvayoor Sathyagraha,  Paliyam  Sathyagraha.  Kuttamkulam  Sathyagraha,  Temple  Entry Proclamation, Temple Entry Act .Malyalee Memorial, Ezhava Memorial etc. Malabar riots, Civil Disobedience Movement, Abstention movement etc.

Role Of Press In Renaissance
Malayalee,  Swadeshabhimani,  Vivekodayam,  Mithavadi,  Swaraj,  Malayala Manorama, Bhashaposhini, Mathnubhoomi, Kerala Kaumudi, Samadarsi, Kesari, AIAmeen, 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  Kuttimalu  Amma,  Lalitha Prabhu.Akkamma Cheriyan, Anna Chandi, Lalithambika Antharjanam and others

Leaders Of Renaissance
Thycaud  Ayya  Vaikundar,  Sree  Narayana  Guru,  Ayyan  Kali.Chattampi  Swamikal, Brahmananda Sivayogi, Vagbhadananda, Poikayil Yohannan(Kumara Guru) Dr Palpu, Palakkunnath Abraham Malpan, Mampuram Thangal, Sahodaran Ayyappan, Pandit K P Karuppan,  Pampadi  John Joseph, Mannathu Padmanabhan,  V T Bhattathirippad, Vakkom Abdul  Khadar  Maulavi,  Makthi  Thangal, Blessed Elias Kuriakose Chaavra, Barrister  G P Pillai,  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 Kesavan. Swami Ananda Theerthan , M C Joseph, Kuttippuzha Krishnapillai and others

Literary Figures
Kodungallur  Kunhikkuttan  Thampuran,  KeralaVarma  Valiyakoyi  Thampuran, Kandathil  Varghese Mappila.  Kumaran Asan,  Vallathol  Narayana Menon,  Ulloor  S Parameswara Iyer, G Sankara Kurup, Changampuzha Krishna Pillai, Chandu Menon, Vaikom Muhammad Basheer.  Kesav Dev, Thakazhi  Sivasankara Pillai,  Ponkunnam Varky, S K Pottakkad and others

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 qualification 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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