Why is Covariance Bounded? The Power of Cauchy-Schwarz Inequality Data Science and A.I.
Why is Covariance Bounded? The Power of Cauchy-Schwarz Inequality Covariance and Standard Deviation Definitions: Sample Covariance: \[ \text{Cov}(X, Y) = \frac{1}{n-1} \sum_{i=1}^n (X_i – \bar{X})(Y_i – \bar{Y}) \] Sample Standard Deviations: \[ \sigma_X = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (X_i – \bar{X})^2}, \quad \sigma_Y = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (Y_i – \bar{Y})^2} \] Cauchy-Schwarz Inequality The Cauchy-Schwarz inequality states: […]
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