Covariance, Correlation & Bivariate Normal Distribution

Connect covariance and correlation to bivariate normal models and prediction. Prerequisites: moments, joint distributions and conditional expectation. Calculate covariance under rescaling, variances of linear combinations and conditional normal probabilities. Analyze feasible covariance matrices, measurement noise, perfect correlation and counterexamples involving normal marginals. Challenges distinguish general moment identities from conclusions that require joint normality.

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Further reading: 5.3.1 Definition and properties, 5.3.2 Joint normal construction and conditional law.