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Principles of Probability & Statistics

Table of Contents

Publisher’s Note




Introduction




Contributors




Mathematical Foundations of Probability and Statistics




Bayes’ Theorem




Binomial Theorem




Bivariate Data




Central Limit Theorem




Chebyshev’s Inequality




Combinations




Combinatorics




Confidence Intervals




Continuous Random Variable




Correlation Modeling




Correlational Research




Correlations and Causations




Density




Descriptive Statistics




Discrete Mathematics




Distributions




Empirical Formula




Expected Values




Exponentials and Logarithms




Function Rate of Change




Functions




Graphs




Histograms




Infinity (Mathematics)




Law of Large Numbers




Limits and Continuity




Linear and Nonlinear Relationships




Linear Concepts




Mathematical Modeling




Matrices




Normal and Binomial Distributions




Normal Distribution




Numbers and Operations




One-Tailed and Two-Tailed t-Tests




Permutations and Combinations




The Poisson Distribution




Polynomials




Probability




Probability and Statistics




Proofs




Randomization




Randomness




Regression Modeling and Analysis




Regression Point Displacement




Scatterplots




Significance Levels




Standard Deviation




Statistics Education




Transformations




Zero




Research Applications of Probability and Statistics




Abductive Reasoning




ANCOVA




ANOVA




BACI




Case Study Research




Causal Networks




Chi-Square Goodness-of-Fit Test




Chi-Square Test of Independence




Chi-Squared Distribution




Cluster Sampling




Comparative Research




Completely Randomized Designs




Cross-Sectional Sampling




Crossover Repeated Measures Design




Data Collection




Deductive Reasoning




Descriptive Research




Experimental Research




Explanatory Research




Exploratory Research




External Validity




Field Experiment




Fractional Factorial Designs




Full Factorial Design




Holistic Study, Ethnography




Hypothesis




Hypothesis-Based Study




Hypothesis Testing




Independent Variable Manipulation




Inductive Reasoning




Inferential Statistics




Interdisciplinary Mathematics Research




Internal Validity (Causality)




Interpretive Methods




Kruskal-Wallis Test




Laboratory Experiment




Latin Square Designs




Longitudinal Sampling




Mann-Whitney U Test




Mill’s Methods of Causal Reasoning




Multiple Case Study




Multistage Sampling




Nested Analysis of Variance




Nested Designs




Nonequivalent Dependent Variables Design




Nonprobabilistic Sampling




Nonresponse Error




Objectivity




Placebo Effect




Plackett-Burman Design




Positivist Methods




Posttest-Only Design




Pretest-Posttest Experimental Research Design




Probabilistic Sampling




Prospective Cohort Design




Quadrat Sampling




Qualitative Research




Quantitative Research




Random Sampling Error




Randomized Complete Block Designs




Regression Discontinuity Design




Replication, Manipulation, and Randomization




Retrospective Cohort Design




Sample Frame Error




Sample Surveys




Sampling Design vs. Experimental Design




Sampling Design: Randomness and Interspersion




Sampling Framework




Sampling vs. Census




Solomon Four-Group Design




Split-Plot Type Designs




Statistical Inference




Stratified Random Sampling / Randomized Block Design




Student’s t-Test




Switching Replications Design




Systematic Sampling




Time-Series Designs




Type I and Type II Errors




Real-World Applications of Probability and Statistics




Betting and Fairness




Birthday Problem




Business Finance




Census




Climate Models and Modeling




Climate Prediction and Projection




Computational Methods for Economics




Data Analysis and Probability in Society




Data Science




Dice Games




Disease Survival Rates




Elections




Forecasting




Game Theory




Genetics and Mathematics




Infectious Diseases, Tracking




Insurance and Mathematics




Interest Rates




Investment Concepts




Market Research and Mathematics




Mathematical Puzzles




Mathematics, Applied




Mathematics, Theoretical




Mathematics in Economics




Mathematics Software




Medical Diagnosis




Numbers and Operations in Society




Observational Data of the Atmosphere and Oceans




Predicting Preferences




Predictive Mathematical Models




Spam Filters




Stock Market Indices




Trading and Markets




Voting Methods




Weather Forecasting: Numerical Weather Prediction




Weather vs. Climate




Bibliography




Glossary




Organizations