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Table of Contents

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Basics

Objectives of Statistics • Statistical Investigation • Statistical Element and Population • Statistical Variable • Measurement Scales • Qualitative Variables • Quantitative Variables • Grouping Continuous Data • Statistical Sequences and Frequencies • Multiple Choice Questions

One-Dimensional Frequency Distributions

One-Dimensional Distribution • Frequency Distribution for Continuous Data • Empirical Distribution Function • Numerical Description of One-Dimensional Frequency Distributions • Location Parameters – Mean Values (2): Harmonic Mean, Geometric Mean • Measures of Scale or Variation • Graphical Display of the Location and Scale Parameters • Multiple Choice Questions

Two-dimensional Frequency Distribution

Introduction • Two-Dimensional Frequency Tables • Graphical Representation of Multidimensional Data • Marginal and Conditional Distributions • Characteristics of Two-Dimensional Distributions • Relation between Continuous Variables (Correlation, Correlation Coefficients) • Relation between Discrete Variables (Rank Correlation) • Relationship between Nominal Variables (Contingency) • Multiple Choice Questions

Regression

Regression Analysis • One-Dimensional Regression Analysis • Multi-Dimensional Regression Analysis • Multiple Choice Questions

Time Series Analysis

Time Series Analysis • Trend of Time Series • Periodic Fluctuations • Quality of the Time Series Model • Multiple Choice Questions

Combinatorics

Introduction • Permutation • Variations • Combinations • Properties of Euler’s Numbers (Combination Numbers) • Multiple Choice Questions

Probability Theory

The Sample Space, Events and Probabilities • Event Relations and Operations • Probability Concepts • Conditional Probability and Independent Events • Theorem of Total Probabilities and Bayes’ Rule • Multiple Choice Questions

Random Variables

The Definition • One-Dimensional Random Variables • One-Dimensional Continuous Random Variables • Parameters • Two-Dimensional Random Variables • Independence • Parameters of Two-Dimensional Distributions • Multiple Choice Questions

Probability Distributions

Important Distribution Models • Uniform Distribution • Binomial Distribution • Hypergeometric Distribution • Poisson Distribution • Exponential Distribution • Normal Distribution • Central Limit Theorem • Approximation of Distributions • Chi-Square Distribution • t - Distribution (Student t - Distribution) • F - Distribution • Multiple Choice Questions

Sampling Theory

Basic Ideas • Sampling Distribution of the Mean • Distribution of the Sample Proportion • Distribution of the Sample Variance • Multiple Choice Questions

Estimation Theory

Estimation Theory • Properties of Estimators • Construction of Estimators • Interval Estimation • Confidence Interval for the Mean • Confidence Interval for Proportion • Confidence Interval for the Variance • Confidence Interval for the Difference of Two Means • Finding the Sample Size • Multiple Choice Questions

Statistical Tests

Key Concepts • Testing Normal Means • Testing the Proportion in a Binary Population • Testing the Difference of Two Population Means • Chi-Square Goodness-of-Fit Test • Chi-Square Test of Independence • Multiple Choice Questions

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