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# OPSC Pre Exam Syllabus : Statistics

Updated on: Apr 18, 2013
Group-A:
Probability & Probability Distributions
Unit-I
Random Experiment, Sample Space, Event, Algebra Of Events, Probability On A Discrete Sample Space, Basic Theorems Of Probability And Simple Examples Based Thereon, Conditional Probability, Independent Events, Bayes Theorem And Its Applications, Discrete And Continuous Random Variables And Their Distributions, Expectation, Moments, Moment Generating Function, Joint Distribution Of Two Random Variables, Marginal And Conditional Distributions, Independence Of Random Variables, Covariance. Chebyshev's Inequality, Weak Law Of Large Numbers And Central Limit Theorem For Independently And Identically Distributed Random Variables With Finite Variance And Their Simple Applications.

Unit-II
Distribution Function Of Random Variables, Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson, Uniform, Beta, Exponential, Gamma, Cauchy, Normal, Lognormal And Bivariate Normal Distributions, Real-Life Situations Where These Distributions Provide Appropriate Models. Derivation Of Mgf And Characteristic Function Of The Distributions, Computation Of Their Moments And Pearsonian Co-Efficients.

Group-B:
Statistical Methods
Unit-I
Concept Of A Statistical Population And Sample, Types Of Data, Presentation And Summarization Of Data, Measures Of Central Tendency, Dispersion, Moments, Skewness And Kurtosis, Measures Of Association And Contingency, Correlation, Rank Correlation, Intraclass Correlation, Correlation Ratio, Simple And Multiple Linear Regression, Multiple And Partial Correlations (Involving Three Variables Only)

Unit-II
Curve-Fitting And Principle Of Least Squares, Concepts Of Parameter And Statistic, Z, C2 , T And F- Statistics And Their Distributions, Properties And Applications, Distributions Of Sample Range And Median (For Continuous Distributions Only).

Group-C:
Statistical Inference
Unit-I
Properties Of A Good Estimator : Unbiasedness, Consistency, Efficiency, Sufficiency, Completeness; Minimum Variance Unbiased Estimation, Rao-Blackwell Theorem, Cramer- Rao Inequality And Minimum Variance Bound Estimator, Methods Of Estimation : Moments, Maximum Likelihood, Least Squares And Minimum Chi-Square; Properties Of Maximum Likelihood Estimator, Idea Of A Random Interval, Confidence Intervals For The Parameters Of Standard Distributions, Shortest Confidence Intervals, Large-Sample Confidence Intervals.

Unit-II
Simple And Composite Hypotheses, Two Kinds Of Errors, Level Of Significance, Size And Power Of A Test, Desirable Properties Of A Good Test, Most Powerful Test, Neyman-Pearson Lemma And Its Application For Testing Simple Hypothesis, Uniformly Most Powerful Test, Likelihood Ratio Test And Its Properties And Applications. Chi-Square Test, Sign Test, Wald- Wolfowitz Run Test, Run Test For Randomness, Median Test, Wilcoxon Test And Wilcoxon- Mann-Whitney U-Test. Wald's Sequential Probability Ratio Test, Oc And Asn Functions, Application To Binomial And Normal Distributions.

Group-D :
Sampling Theory And Design Of Experiments

Unit-I
Complete Enumeration Vs Sampling, Need For Sampling, Basic Concepts Of Sampling And Sampling Design, Large-Scale Sample Surveys, Sampling And Non-Sampling Errors, Simple Random Sampling, Estimation Of Sample Size, Stratified Random Sampling, Systematic Sampling, Cluster Sampling, Ratio, Product And Regression Methods Of Estimation Under Simple And Stratified Random Sampling, Double Sampling For Ratio And Regression Methods Of Estimation, Two-Stage Sampling With Equal Size First-Stage Units.

Unit-II
Analysis Of Variance With Equal Number Of Observations Per Cell In One, Two And Threeway Classifications, Analysis Of Covariance In One And Two-Way Classifications, Basic Principles Of Experimental Designs, Completely Randomized Design, Randomized Block Design, Latin Square Design, Missing Plot Technique, 2n Factorial Experiment, Total And Partial Confounding, 32 Factorial Experiments, Split-Plot Design And Balanced Incomplete Block Design.
Each Group Should Have Equal Weight

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