Univariate Analysis

Empirical Cumulative Distribution Function

Inverse Cumulative Distribution Function

Empirical Probability Mass Function

Measures of Central Tendency

Mean

Sample Mean

Sample mean is unbiased

Robustness

Median

Mode

Measures of Dispersion

Range

Interquartile Range

Sample Variance

Geometric Interpretation of Sample Variance

Sample Variance is biased but asymptomatically Unbiased

Bivariate Analysis

Empirical Joint Probablitiy Mass Function

Measures of Location and Dispersion

Mean

Variance

Covariance

Correlation

Geometric Interpretation of Sample Sovariance and Correlation

Covariance matrix

Multivariate analysis

Mean

Covariance Matrix

Covariance Matrix is positive semidefinite

• \(a^T\Sigma a \ge 0\)

Total and Generalized Variance

Sample Covariance Matrix

Data Normalization

Range Normaliziation

Standard Score Normalization

Normal Distribution

Univariate Normal Distribution

Probability Mass

Multivariate Normal Distribution

Total and Generalized Variance