## Sunday, August 21, 2016

### Covariance formula with CDF (Hoeffding's Covariance Identity)

A complete proof of above lemma can be found on page 241 (Lemma 7.27) of Quantitative Risk Management: Concepts, Techniques and Tools.

Hint: 2$$cov(X_1, X_2) = E[(X_1-\tilde{X_1})(X_2-\tilde{X_2})]$$,
where $$(\tilde{X_1}, \tilde{X_2})$$ is an independent copy with the same joint distribution function as  $$(X_1, X_2)$$.