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Mathematical Statistics I

by: Vance Bode Sr.

Mathematical Statistics I 22S 153

Vance Bode Sr.
GPA 3.72


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This 3 page Study Guide was uploaded by Vance Bode Sr. on Friday October 23, 2015. The Study Guide belongs to 22S 153 at University of Iowa taught by Staff in Fall. Since its upload, it has received 42 views. For similar materials see /class/228090/22s-153-university-of-iowa in Natural Sciences and Mathematics at University of Iowa.

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Date Created: 10/23/15
Updated September 26 2008 Study Guide for the Minor in Statistics Mathematical Statistics 22S153154 This is a ThreeHour Examination You are allowed to consult either four singlesided or two doublesided 85 X 11 crib notes use your own nongraphing calculator Study the following topics 1 Probabili Spaces a Sample Spaces and Events b Axioms c Properties Conditional Probability and Y 39 39 a De nition and Properties b Bayes Theorem Random Variables a De nition b Discrete Continuous and Mixed c Cumulative Distribution Function d Probability Density Function Probability Mass Function Moments and Quantiles of General Tquot quot a mean median quantiles b variance Special Discrete Distributions a Binomial b Hypergeometric c Poisson d Geometric and Negative Binomial e Moments of these Special Continuous Distributions a Normal b Gamma including exponential and chisquare c Weibull d Uniform e Lognormal f Cauchy g Student s t h F i Moments of these Multivariate Distributions De nition Bivariate Normal Multinomial Joint and Marginal Distributions Conditional Distributions and Independence Covariance and Correlation Conditional Mean and Variance PWFDFF U Generating Functions a Moment Generating Functions b Obtaining Moments from Generating Functions c Moment Generating Functions of Special Distributions d Moment Generating Functions of Sums of Independent Random Variables Functions of Random Variables a Distributions Function Technique b Change of Variable Technique c Moment Generating Function Technique d Expectations of Functions of Random Variables e Linear Combinations of Random Variables f Order Statistics de nition and distributions Convergence Concepts Convergence in Probability Convergence in Distribution Laws of Large Numbers Central Limit Theorem 9957 Estimation a Maximum Likelihood b Method of Moments c Bayes Estimation d Fisher Information e Interval Estimation Con dence Intervals for Proportions Means Variance f Decision Theory and Bayesian Methods g Methods of evaluating estimators Mean Square Error Consistency Bias Hypotheses Tests De nition of Tests of Statistical Hypotheses NeymanPearson Lemma Power Functions Uniformly Most Powerful Tests Likelihood Ratio Tests ChiSquare Tests including Contingency Tables hog057 Suf cient Statistics a De nition b Factorization Theorem c RaoBlackwell Theorem d Completeness and Uniqueness e EXponential Families f Sufficiency and Independence


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