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Descriptive Statistics and Probability (BM Statistics)

Content of the Lecture

Introduction

  • Population
  • Variables
  • Scales of Measure

Analysis of One-Dimensional Data

  • Univariate Frequency Distribution
  • Discrete and Continous Classified Data
  • Cumulative Distribution Function
  • Quantiles
  • Box Plot
  • Measures of Location
    • Mode
    • Median
    • Arithmetic Mean
    • Aggregation Theorem for Means
    • Trimmed Arithmetic Mean
  • Measures of Dispersion
    • Range
    • Interquartile Range
    • Variance
    • Standard Deviation
    • Variance Decomposition
    • Gini Mean Difference

Measurement of Concentration and Inequality

  • Curve of Concentration
  • Rosenbluth Index
  • Herfindahl Index
  • Lorenz Curve
  • Gini Coefficient
  • Coefficient of Variation

Indices

  • Index Types: Laspeyres Indices, Paasche Indices and Fisher Indices
  • Index Numbers: Price Indices, Volume Indices and Value Indices
  • Aggregation of Subindices
  • Consumer Price Indices

Analysis of Multidimensional Data

  • Marginal Distribution
  • Conditionial Distribution
  • Descriptive Independence
  • Covariance
  • Coefficient of Correlation
  • Spearman’s Rank Correlation Coefficient
  • Pearson’s Contingency Coefficient

Random Experiments and Probability

  • Random Experiments
    • Sample Space
    • Events and their Linkage
  • Probabilities
    • Formal Definition of Probability
    • Laplace Experiments
    • Basic Rules of Probability and Combinatorics
  • Conditional Probability
    • Conditional Probability
    • Total Probability and Bayes' Theorem
    • Independence of Events

Random Variables and Distributions

  • Random Variables
    • Cumulative Distribution Function
    • Quantile Function
    • Discrete Random Variables
    • Continuous Random Variables
    • Affine-Linear Transformation of Random Variables
  • Distribution Parameter
    • Expected Value
    • Variance
    • Tchebychev Inequality