# Proof of variance reduction of bagging

In Lecture 4 of the following course:

Advances in Financial Machine Learning: 10 Lectures


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