Kerala PSC Statistician Syllabus 2023: Download pdf, Check Exam Pattern | കേരള PSC സ്റ്റാറ്റിസ്റ്റിഷ്യൻ സിലബസ് 2023

Kerala PSC Statistician Syllabus: Kerala Public Service Commission has released the Kerala PSC Exam Calendar April 2023. In this article we will provide the detailed syllabus of the upcoming Kerala PSC Statistician Exam 2023. In order to crack the exam, one needs to have a clear understanding of the syllabus, therefore read through Statistician Kerala PSC Syllabus to broaden your perspective. You can also download Statistician PSC Syllabus in pdf format.

Kerala PSC Statistician Syllabus

Kerala PSC Statistician Syllabus: പരീക്ഷയ്ക്കുള്ള തയ്യാറെടുപ്പുകൾ ആരംഭിക്കാൻ  സമയമായി. പരീക്ഷയിൽ വിജയിക്കുന്നതിന്, സിലബസിനെക്കുറിച്ച് വ്യക്തമായ ധാരണ ഉണ്ടായിരിക്കണം, അതിനാൽ സ്റ്റാറ്റിസ്റ്റിഷ്യൻ സിലബസ് വിശദമായി വായിച്ച് മനസിലാക്കുക. നിങ്ങൾക്ക് Statistician PSC Syllabus pdf രൂപത്തിൽ ഡൗൺലോഡ് ചെയ്യാം.

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ചുവടെ നൽകിയിരിക്കുന്ന പട്ടികയിൽ Statistician Kerala PSC സംബന്ധമായ എല്ലാ പ്രധാനപ്പെട്ട വിവരങ്ങളും ലഭിക്കും.

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Kerala PSC Statistician Exam Pattern

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Kerala PSC Statistician Detailed Syllabus

Part I: Probability Theory 

• Concepts of probability, independence of events, addition theorem, multiplication theorem, conditional probability and Bayes theorem. Discrete and continuous random variables, distribution function, density function, probability generating function, moment generating function, characteristic function, inversion formula and uniqueness theorem, expectation of random variables and its properties, moments, cumulants.
• Convergence: Modes of convergence, Convergence in probability, in distribution, in rth mean, almost sure convergence and their inter-relationships.
• Laws of Large Numbers: Kolmogorov’s inequality, Weak law of large numbers (Khinchine’s and Kolmogorov’s), Kolmogorov’s strong law of large numbers, Central limit theorems(CLT) for i.i.d random variables, Lindberg-Levy CLT, Liaponov’s CLT, Lindberg-Feller CLT.

Part II. Statistical Estimation Theory

• Point estimation: Sufficiency and minimal sufficiency, Exponential family of distributions, Factorization criterion. Unbiased estimation, Completeness, Ancillary statistics and Basu’s theorem, UMVUE estimators and their characterizations, Rao-Blackwell Theorem, Lehmann Scheffe Theorem, Fisher information measure and its properties, Cramer-Rao inequality. Consistent estimators, mean square error, CAN estimator.
• Methods of estimation: Methods of moments, Maximum likelihood estimation, Least square estimation and their properties.
• Bayesian Estimation: Loss function, prior distribution, Bayes theorem, posterior distributions, Bayes risk, Bayes principle, Bayes estimators.
• Interval Estimation: Large sample confidence intervals, UMA and UMAU confidence intervals, Shortest expected length confidence intervals, construction of confidence intervals using pivots.

Part III. Testing of hypothesis 

• Fundamental concepts of testing of hypothesis, Neyman-Pearson lemma, UMP tests, unbiased tests and UMPU tests, unbiased critical regions and similar regions, likelihood ratio tests, construction of sequential probability ratio tests, Wald’s identity, OC and ASN functions, Properties of SPRT.
• Non-parametric inference: Goodness of fit tests- Chi square test and Kolmogorov Smirnov test, Sign test, Signed rank test, Run test, Median test, Mann-Whitney U-test, Wilcoxan test, Kruskall Wallis test

Part IV. Design of Experiments 

• Basic principles of design of experiments, Gauss Markoff Theorem, CRD, RBD and LSD, Balanced Incomplete Block designs, Partially balanced incomplete block designs, Lattice designs, Analysis of co-variance for completely randomized and randomized block designs. Analysis of experiments with missing observations.
• Factorial Designs: Principles, factorial Designs (2 factor, General factor, 2k factorial), Confounding techniques- Partial and Total, fractional factorial design.

Part V. Sampling Theory 

• Population, sample, sampling design, simple random sampling (SRS with replacement and without replacement, stratified random sampling, systematic sampling, cluster sampling, ratio estimators, regression estimators, probability proportional to size with replacement sampling, varying probability without replacement (Midzuno-Sen-Lahiri sampling strategy, Desraj, Horvic’s Thompson, Murthy’s), multiphase and mutistage sampling.

Part VI. Distribution Theory 

• Univariate random variables, distribution functions and their properties, bivariate distributions joint, marginal and conditional distribution, independence of random variables.
• Discrete distributions- binomial, Poisson, negative binomial, geometric, uniform, hyper
  geometric, power series and multinomial distributions.
• Continuous distributions- uniform, normal, exponential, double exponential, beta, gamma, Cauchy, Weibull, Pareto, log-normal and logistic distributions, Pearson system of distributions.
• Order Statistics- Joint, marginal and conditional distributions of order statistics of a random sample arising from continuous distributions, distribution of sample median and range
• Sampling distributions- distribution of the mean and variance of a random sample from normal population, Chi-square, t, and F distributions.

Part VII. Multivariate Analysis

• Concepts of multivariate distributions, multivariate normal distribution(MND), marginal and conditional distributions, characteristic function of MND, estimation of mean vector and covariance matrix, Wishart distribution and its properties, distribution of simple, partial and multiple correlations based on samples from normal population, Hotelling’s T2 and Mahalanobis D  statistics and their properties, multivariate Fisher Behren’s problem, testing independence of sets of variates, testing equality of covariance matrices and means, sphericity tests, testing the hypothesis that a covariance matrix equal to given matrix.
• Classification problem, procedures of classification into one of two populations with known probability distributions, classification into one of two known multivariate normal populations, classification into one of several populations, principal component analysis and its properties, canonical variables and canonical correlations, factor analysis.

Part VIII. Stochastic Process 

• Concept of Stochastic processes, examples, specifications, Markov chains, transition probability matrix, Chapman Kolmogorov equations, recurrence, transience and periodicity of states, classification of states, limiting probabilities, stationary distribution, ergodic theorem.
• Gamblers ruin problem and random Walk, branching processes (discrete time), probability of ultimate extinction.
• Continuous time Markov Chains: counting process – inter arrival time and waiting time
  distributions. Poisson processes and properties, conditional distribution of arrival times,
  Generalization of Poisson processes (non-homogenous Poisson process, compound Poisson process, conditional mixed Poisson process), birth and death processes and applications to queueing models, Markovian queues, M/G/1, G/M/1 queues, multi server queues.
• Renewal processes, renewal theorems and their applications, renewal reward process,
  regenerative processes, Brownian motion processes.

Part IX. Regression Analysis

• Linear Regression Model, least squares estimation, Gauss Markov setup, properties of the estimates, maximum likelihood estimation, generalised least squares, Hypothesis testing – likelihood ratio test, F-test. Confidence intervals.
• Residual analysis, collinearity, non-constant variance and serial correlation, departures from normality, diagnostics and remedies
• Polynomial regression in one and several variables, orthogonal polynomials, indicator variables, subset selection of explanatory variables, stepwise regression.
• Nonlinear regression, estimation and diagnosis methods for logistic and Poisson regressions.

Part X. Mathematical Methods for Statistics

• Riemann-Stieltjes Integral- definition, existence and properties, integration by parts, change of variable – Step functions as integrators. Reduction to finite sum, Improper integrals- Gamma and Beta integrals.
• Point wise convergence and uniform convergence of sequences and series of functions.
• Multivariable functions, limit and continuity of multivariable functions, derivatives, directional derivatives and continuity, total derivative in terms of partial derivatives, optima of multivariable functions.
• Elementary matrices, determinants, rank of a matrix, inverse, diagonal reduction, transformations, idempotent matrices, solution of linear equations, characteristic roots and vectors, Cayley- Hamilton theorem, algebraic and geometric multiplicity of characteristic roots, spectral decomposition, quadratic forms, classification and reduction of quadratic forms, generalized inverse, Moore-Penrose inverse- definition and existence, properties of generalized inverse.

Kerala PSC Statistician Syllabus 2023- Download Pdf

Kirtads Statistician Syllabus Pdf ചുവടെ നൽകിയിരിക്കുന്ന ലിങ്ക് വഴി ഡൗൺലോഡ് ചെയ്യാവുന്നതാണ്.

Kerala PSC Statistician Syllabus 2023- Download Pdf

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