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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