Applied Statistical Methods

¿PrefaceAcknowledgmentsChapter 1 Introduction 1.1 Why Statistical Methods? 1.2 Advice to the StudentChapter 2 The Frequency Distribution-A Tool and a Concept 2.1 Introduction 2.2 An Example of a Frequency Distribution 2.3 Frequency Class Nomenclature and Tabulation 2.4 Discrete versus Continuous Data 2.5 Graphical Representation of a Frequency Distribution 2.6 The Cumulative Frequency Graph 2.7 What a Frequency Distribution Shows 2.8 Some Examples of Use of Frequency Tables and Graphs 2.9 Sample versus Population 2.10 Summary ProblemsChapter 3 Summarization of Data by Objective Measures 3.1 Introduction 3.2 Some Averages 3.3 Some Measures of Variability 3.4 Efficient Calculation of Averages and Standard Deviations 3.4.1 Calculations for Frequency Data 3.5 Further Descriptive Measures of Frequency Distributions, Third and Fourth Moments 3.6 Summary ProblemsChapter 4 Some Elementary Probability 4.1 Introduction 4.2 Sample Spaces of Outcomes 4.3 Events 4.3.1 Relations of Events 4.3.2 Combinations of Events 4.4 Probabilities of Events 4.5 Probabilities on Discrete Sample Spaces 4.5.1 Countably Infinite Spaces 4.5.2 Events over Discrete Spaces 4.6 Independent and Dependent Events 4.6.1 Conditional Probabilities 4.6.2 Repeated Trials 4.7 Discrete Probabilities 4.7.1 Permutations and Combinations 4.7.2 Discrete Probability Examples 4.8 Probabilities on Continuous Spaces 4.9 Applied Bayes' Probabilities-Posterior Probabilities 4.10 Interpretation of a Probability 4.11 Random Variables 4.12 Summary ProblemsChapter 5 Some Discrete Probability Distributions 5.1 Theoretical Populations 5.2 Discrete Probability Distributions in General 5.2.1 Expected Values for Y and Functions of Y 5.2.2 Population Curve-Shape Characteristics 5.2.3 Algebra of Expectations 5.2.4 Further on Population Moments 5.3 The Binomial Distribution 5.3.1 Examples of the Binomial Distribution 5.3.2 Population Moments for Binomial Distributions 5.3.3 Use of Binomial Tables 5.3.4 Calculation of a Binomial Distribution 5.3.5 Approximations to the Binomial Distribution 5.3.6 Conditions of Applicability of the Binomial Distribution 5.4 The Poisson Distribution 5.4.1 A Derivation of the Poisson Probability Function 5.4.2 Examples of the Poisson Distribution 5.4.3 Tables of the Poisson Distribution 5.4.4 Using the Poisson Distribution to Approximate the Binomial 5.4.5 Derivation of the Poisson as a Limit of the Binomial 5.4.6 Conditions of Applicability of the Poisson Distribution 5.5 The Hypergeometric Distribution 5.5.1 Tables for the Hypergeometric Distribution 5.5.2 Examples of the Hypergeometric Distribution 5.5.3 Moments for the Hypergeometric Distribution 5.5.4 Binomial Approximations to the Hypergeometric Distribution 5.5.5 Poisson Approximations to the Hypergeometric Distribution 5.5.6 Approximations to Sums of Terms of the Hypergeometric Distribution 5.5.7 Conditions of Applicability of the Hypergeometric Distribution 5.5.8 Applications of the Hypergeometric Distribution 5.6 The Uniform Distribution 5.7 The Geometric Distribution 5.8 The Negative Binomial Distribution 5.9 Generating Samples from Discrete Distributions 5.10 Summary References ProblemsChapter 6 Some Continuous Probability Distributions 6.1 Continuous Probability Distributions 6.2 Some General Properties of Continuous Distributions 6.2.1 Moments for a Continuous Distribution 6.3 The Normal Curve 6.3.1 Properties of the Normal Distribution 6.3.2 The General Normal Curve 6.3.