TNPSC Mains Syllabus for Optional Subject: Statistics
UNIT I: Uses, Scope and limitation of Statistics, Collection, Classification and Tabulation of data, Diagramatic and Graphical representation, Measures of location, dispersion, Skewness and Kurtosis – Correlation and regression – Curve Fitting –
Linear and Quadratic equation by the method of least squares.
UNIT II: Probability - Addition, Multiplication and Baye’s Theorems and their application. Tchebychev’s inequality. Random variables – Univariate and Bivariate –
Probability distributions – Marginal and conditional distributions – Expectations – Moments and cumulants generating functions.
UNIT III: Probability distributions – Binomial, Poisson, Geometric and Hypergeometric. Continuous distributions – Uniform, exponential and normal. Sampling distributions and standard error, student’s ‘t’, Chi-square and F statistic – distributions and their applications.
UNIT IV: Estimation – Point estimation – properties of estimates Neyman – Fisher Factorization theorem(without proof) Cramer – Rao inequality, Rao – Blackwell theorem – MLE and method of Moments estimation – Interval estimation – for population mean and variance based on small and large samples.
UNIT V: Tests of Hypothesis – Null and Alternative – Types of errors – Power of test, Neyman – Pearson lemma, UMP and Likelihood ratio tests, Test procedures for large and small samples – Independence of attributes, Chi-square test – Goodness of fit
UNIT VI: Simple random sample – stratified, systematic, Cluster (Single stage)
Estimation of mean and variance in SKS – Sample Survey – Organisation – CSO and NSSO – Sampling and Non-Sampling errors.
Analysis of Variance – Principles of design CRD, RBD and LSD – Factorial experiments 22, 23 and 32
(Without confounding) Missing plot techniques.
UNIT VII: Concept of SQC – Control Charts – X, R, p and charts Acceptance sampling plan – single and double – OC curves Attributes and Variables plan.
OR Models – Linear Programming problems – Simplex method Dual – Primal,
Assignment problems, Net work – CPM and PERT
UNIT VIII: Time series – Different components – Trend and Seasonal Variations –
Determination and elimination
UNIT IX: Index Numbers – Construction and uses – Different kinds of simple and weighted index numbers – Reversal tests – construction and use of cost of living index numbers – Birth and death rates – Crude and standard death rates, Fertility rates – Life table construction and uses.
UNIT X: Statistical Computing using Excel – Understanding on the usage of Statistical Packages including SPSS, MINITAB and SAS.
