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UPPSC 2010 Syllabus for Statistics (Subject Code 15):

Paper I

Probability Theory and Statistical Application

Group - A

Probability Theory: Sample Space and Events, Classical and Axiomatic Definitions of Probability. Properties of Probability Measure, Conditional Probability, Independence of Events, Bayes Theorem and its Applications. Random Variable and its Distribution Function, Elementary Properties of Distribution Function, Discrete and Continuous Random Variables, Vibariate Distribution and Associated Marginal and Conditional Distributions-Expectation, Moments.

Moment Generating and Characteristic Functions, Markov and Chebyshev Inequalities, Convergence in probability, Weak Law of Large Numbers and Central Limit Theorem for independently and Identically Distributed Random Variables. Some standard Discrete and Continuous Distributions, viz., Bionomial. Poisson. Hypergeometric, Geometric Negative Bionomial, Multinomial, Uniform. Normal, Exponential, Gamma. Beta and Cauchy. Bivariate Normal Distribution.

Group - B

Statistical Applications: Linear Regression and Correlation, Product Moment correlation, Rank Correlation. Intra-Class Correlation and Correlation Ratio, Multiple and Partial Correlational and Regression for Three Variables. Principles of Experimental Design, One-Way and Two-Way Analysis of Variance with Equal number of Observations per Cell, Completely Randomized Design, Randomized.

Block Design, Latin Square Design, 2' and 23 Experiments, Missing Plot Technique. Sources of Demographic Data, Stable and Stationary Populations, Measures of Fertilty and Mortality, Life Tables, Simple Populations. 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-Edgeworth and 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. Penodogram and Correiogram Analysis, Variate Difference Method.

Paper - II

Statistical Inference: and Management:

Group - A

Statistical Inference:

Properties of Estimators, Consistency, Unbiasedness. Efficiency, Sufficiency and Compltences, Cramer-Rao Bound, Minimum Variance Unbased Estimation, Rao-Blackwell Theorem. Estimation. Simple and Composite Hypotheses. Two Kinds to Errors, Critical Region, Level of Significance, Size

5. Function. Unbased Tests, Most Powerful and Uniformly Most Powerful Tests. Neman-Pearson Lemma and its Applications, Likelihood Ratio Tests. Tests based on t.x2. z and F-distributions, Large Sample Tests. abilizing Transformations. Distributions of Order Statistics and Range, Non- parametric Tests, Viz..Sign Test, Median Test, Run Test, Wifcoxon-Mann- Whitney Test.

Group - B

Statistical Management: Nature of Operations Research Problems, Linear Programming Problem and the Graphical Solution in simple Cases, Simplex Method, Dual of Linear Programming Problem, Allocation and Transporisticn Problems. Zero sum two-person game, Pure and Mixed Strategies, Value of a Game, Fundamental Theorem, Solution of 2x2 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 and Regression Methods of Estimation 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.p and 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 Items, Test Scores. Qualitative Judgements. Theory of Tests, Parallel Tests, True Score, Reliability and Validity of Tests.

UPPSC Main Exam 2010 Syllabus for Statistics