UPPSC Statistics Syllabus
Probability Theory and Statistical Application
Probability Theory: Sample Space and Events, Classical and Axiomatic Definitions ofProbability. Properties of Probability Measure, Conditional Probability, Independence of Events, Bayes Theoremand its Applications. Random Variable and its Distribution Function, Elementary Properties of Distribution Function, Discrete and Continuous Random Variables, Vibariate Distribution and AssociatedMarginal and Conditional Distributions-Expectation, Moments, Moment Generating and Characteristic Func-tions, Markov and Chebyshev Inequalities, Convergence in probability, Weak Law of Large Numbers andCentral Limit Theorem for independently and Identically Distributed Random Variables. Some standard Dis-crete and Continuous Distributions, viz. Bionomial, Poisson, Hypergeometric, Geometric Negative Bionomial, Multinomial, Uniform, Normal, Exponential, Gamma, Beta and Cauchy. Bivariate Normal Distribution.
Statistical Applications: Linear Regression and Correlation, Product Moment correlation, Rank Correlation, Intra-class Correlation and Correlation Ratio, Multiple and Partial Correlational and Regres-sion for Three Variables. Principles of Experimental Design, One-Way and Two-Way Analysis of Variancewith Equal number of Observations per Cell, Completely Randomized Design, Randomized Block Design, Latin Square Design, 2 2 and 2 3 Factorial Experiments, Missing Plot Technique. Sources of Demographic Data, Stable and Stationary Populations, Measures of Fertility and Mortality, Life Tables, Simple Poputations, Measures of Fertility and Mortality, Life Tables, Simple Population Growth Models and Population Projection Techniques. Index Numbers, and their Uses, Index Numbers due to Laspeyre, Paasche, Marshall-Edgeworthand Fisher, Tests for Index Numbers, Construction for Price Index Number and Cost of living Index Number. Times Series and its Components, Determination of Trend and Seasonal Indices, Periodogram and CorrelogramAnalysis, Variate Difference Method.
Statistical Inference And Management group
Statistical Inference: Properties of Estimators, Consistency, Unbiasedness, Efficiency, Sufficiency and Compltences, Cramer-Rao Bound, Minimum Variance Unbased Estimation, Rao-Blackwell Theo-rem. Estimation Procedures, Method of Moments and Method of Maximum Likelihood, Properties of Estima-tors, Interval Estimation. Simple and Composite Hypotheses, Two Kinds fo Errors, Critical Region, Level ofSignificance, Size and Power Function, Unbased Tests, Most-Powerful and Uniformly Most Powerful Tests, Neyman-Pearson Lemma and its Applications, Likefihood Ratio Tests. Tests based on t, x 2, z and F-distribu-tions, Large Sample Tests, Variance Stabilizing Transformations. Distributions of Order Statistics and Range, Non-parametric Tests, Viz…Sign Test, Median Test, Run Test, Wilcoxon-Mann-Whitney Test.
Statistical Management: Nature of Operations Research Problems, Linear ProgrammingProblem and the Graphical Solution in simple Cases, Simplex Method, Dual of Linear Programming Problem, Allocation and Transportstion Problems. Zero sum two-person game, Pure and Mixed Strategies, Value of a Game, Fundamental Theorem, Solution of 2 × 2 Games. Nature and Scope of Sample Survey, Sampling vs. Complete Enumeration, Simple Random Sampling from Finite Populations with and Without Replacement, Stratified Sampling and Allocation Principles, Cluster Sampling with Equal Cluster Size. Ratio, Product andRegression Methods of Esitmation and Double Sampling, Two Stage Sampling with Equal First Stage Units, Systematic Sampling. Statistical-Quality Control, Control Charts for Variables and Attributes (R) (-s), p. n. Pand C Charts.
Acceptance-Sampling, OC, ASN and ATI Curves, Producers risk and Consumer's risk, Concept of AQL, AOQL and LTPD, Single and Double Sampling Plans. Scaling Procedures, Scaling of Test ltems, Test Scores, Qualitative Judgements, Theory of Tests, Parallel Tests, True Score, Reliability and Validity of Tests.