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In Lecture 4 of the following course:

Advances in Financial Machine Learning: 10 Lectures
by Marcos Lopez de Prado

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in the proof of variance reduction for a bagged estimator at page 8, I do not understand why we have the following equality: $$ \sum_{j \neq i}^{N} \bar{\sigma}^2 \bar{\rho} = \sum_{j \neq i}^{N} \sigma_i \sigma_j \rho_{i,j} $$

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