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Statistics (Subject Code 18)

I. Probability Theory (20%): Sample space and events, classical and Axiomatic Definitions of probability, simple Theorem on probability, conditional probability, Bayes Theorem, Independence of Event, Random variable and its Distribution Function Discrete and continuous Random variables, Bivarite Distribution and Associated Marginal and Conditional Distributions independence of Ramdom Variables, Expectation Moments, Moment, Generating Function Chebyshev's Inequality and Applications, Binominal Poisson Negative Binomial, Uniform, Normal Exponential and Bivarlate Normal Distributions.

II. Statistical Methods (20%): Classification, Tabulation and Diagrammatic Representation of Data Measures of Central Tendency, Dispersion, Skewness and Kurlosis, their Merits and Dmerits, Measures of Association and Contingency Linear Regression and Correlation, for two variables, Rank correlation, Intra-ciass correlation, correlation ratio, multiple and Partial Correlation and regression for three variable, curve fitting by least squares method.

III. Statistical Inference (20%): Properties of Estimators, Consistency, Unbiasedness, Efficiency, Sufficiency, Cramer-Rao Inequality, Estimation procedures-Method of Moments, Method of Maximum Likelihood and Method of Least Squares, Interval Estimation, Test based on t, X2 Z and F large samples tests.

Simple and composite Hypotheses, Two kind of errors, Critical Region, Level of Significance, Size and Power Function, Unbiased Tests, Most Powerful and Uniformly Most Powerful Tests. Neyman-Pearson Lemma and its applications.

IV. Sampling theory and Design of Experiments (20%): Sampling theory, sampling units and sampling frames, sampling and non-sampling errors, sampling Vs complete Enumeration, Simple Random sampling from finite populations with and without Replacement Stratified sampling cluster sampling (equal cluster size case) Rational Regression method of estimation Principles of Experimental Design, One way and Two way analysis of variance with equal number of observation per cell, completely Randomized Design, Randomized Block Design, Latin square Design, 2 and 2 Factorial experiments missing plot technique.

V. Applied Statistics (20%): Statistical quality control, Control charts for variables and attributes (X, R) (X s) p, np and C chart, Sources of demographic data, Measures of Fertility and mortality, life table. Index numbers and their uses, tests for index numbers, cost of living, index number.

Time series and its components, determination of trend and seasonal indices:

UPPSC - Combined Lower Subordinate Services Exam 2009 Statistics Syllabus