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Uttar Pradesh Public Service Commission (UPPSC)
Syllabus - Prelims
Statistics
18. Statistics
I. Probability Theory (25%) :
Sample and Events, Classical and axiomatic Definitions of Probability, simple Theorems
on probability, Conditional Probability, Bayes Theorem, Independence of Events, Random Variable and its Distribution Function, Discrete and Continuous Random Variables, Bivariate Distribution and Associated Marginal and Conditional Distribution, Independence of Random Variables, Expectation, Moments, Moment Generating Function, chebyshev’s Inequality and Applications, Binomial Poission, Hypergeometric, Geometric, Negative Binomial, Uniform, Normal Exponential, Gamma, Beta, Cauchy and Bivariate Normal Distribution.
II. Statistical Methods (25%) : Classification, Tabulation and Diagrammatic Representation of Data, Measure of Central Tendency, Dispersion, Skewness and Kurtosis, Their Merits and Demerits, Measures of Association and Contingency, Linear Regression and Correlation for Two variables, Rank Correlation, Intra-class Correlation Ratio, Curve Fitting by Least Squares Method. | |
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III. Statistical Inference (25%) : Properties of Estimators, Consistency, Unbiasedness, Efficiency, Sufficiency, Cramer-Rao Inequality, Best Linear Unbiased Estimate, Estimation Procedures-Method of Moments, Method of Maximum Likelihood and Method of Least Squares, Interval Estimation. Simple and Composite Hypotheses, Two Kinds 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. Statistical Applications (25%) : Concept of Parameter and Statistic, Sampling Distributions (t, x2, Z and F), Tests based on t, x2, Z and F. Large Sample Tests. Sampling Theory, Sampling Units and Sampling Frames, Sampling and Nonsampling Errors. Sampling vs. Complete Enumeration, Simple Random Sampling from Finite Populations With and Without Replacement, Stratified Sampling, Cluster Sampling (Equal Cluster Size Case), Ratio, Product and Regression Methods of Estimation, 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, 22 and 23 Factorial Experiments, Missing Plot Technique. 
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