TNPSC Statistics Exam Syllabus : Tamil Nadu Public Service Commission

Organisation : Tamil Nadu Public Service Commission (TNPSC)
Exam Name : TNPSC Statistics Examination
Standard : PG Degree Standard
Code : 251
Announcement : TNPSC Statistics Exam Syllabus
Website : https://www.tnpsc.gov.in/English/new_syllabus.html

TNPSC Statistics Exam Syllabus

TNPSC Statistics Exam Syllabus are given below,

Related / Similar Syllabus : TNPSC Rehabilitation Science Exam Syllabus

Unit – I: Probability and Random Variables
Instruction to probability: Random Experiments, Sample Space and events, Definition of
probability. Classical, Empirical and Axiomatic approach to probability; Addition and Multiplication Theorem, Conditional probability and Baye’s Theorem. Random Variables and Distribution function, Distribution Function of a vector and a set of infinitely many Random Variables – Mathematical Expectation and conditional Expectation. Convergence in Probability – Weak Law of large Numbers and strong law of large Number – Central limit Theorem – Chebysher’s inequality.

UNIT – II: Distributions
Introduction to Distributions: Marginal and conditional distributions – Generating
functions: – MGF, PGF and CGF – Characteristic function.
Discrete distributions: Binomial, Poisson, Negative binomial and Hyper geometric distribution.
Continuous Distributions: Joint – Marginal – and conditional distributions. Uniform, Normal, Cauchy, Beta, Gamma, Log-Normal, Exponential, Chi-Square, t and F distributions and their properties.

UNIT- III: Estimation Theory
Introduction to Estimation Theory: Unbiasedness, Consistency, Efficiency, Sufficiency
and Completeness.
Theorems and Inequalities: Cramer Rao inequality, Chapma-Robin inequality, Rao – Blackwall Theorems, Lehman – Scheffe, Theorem (with examples), – Factorization
theorem.
Methods of Estimation: Method of moments, Method of Maximum Chi-Square, Method of
Least Square, Bayesian Estimation (with example) – Confidence Intervals for Large and
Small Samples.

UNIT – IV: Testing of Hypothesis and Non-Parametric tests
Introduction to Testing of Hypothesis: Simple Null hypothesis, Alternative hypothesis,
composite hypothesis, two kinds of Errors – Critical Region – Power function.
Tests: Most Powerful test, Neyman – Peerson Lemma: UMP and Unbiased test, MLR
Property and its uses for construction of UMP tests.
Non – Parametric test: Run test – Median test, Sign test – Mann – Whitney test –
Wilcoxon test – Komogrov – Smirnov test (one and two sample test procedures), SPRT Test.

UNIT – V: Regression Analysis
Simple and Multiple Regression model: Description of Data Model – Estimation and Test
of Hypothesis on Regression Coefficient – Index of fit – Predicated Values and Standard error – Evaluation of Fit – Analysis of Residuals.
Multi – collinearity and its effects on inference and forecasting – Selection of variables –
Forward Selection and backward elimination procedures (step wise method).

UNIT – VI: Sampling Theory
Introduction to the theory of Sampling: Sampling designs – estimation procedures – properties of estimations – SRSWOR – Properties of SRSWOR Systematic, Stratified, Ratio and Regression Sampling methods and Estimate of Double Sampling – Sampling and non – sampling errors – Cluster sampling – Two stage and Multistage sampling – sampling and sample survey organizations – CSO and NSSO.

UNIT – VII: Design of Experiments
Contrasts – linear Constraints – Orthogonal contrasts – linear models – fixed effect model
– random effect model – mixed effect model. Principles of CRD, RBD, LSD, 2 n and 3n factorial experiments and split plot Design. Partial and complete confounding – BIBD – Youden Square design – Lattice designs. PBIBD: Construction and Analysis.

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