# Variance of the sum of product of two correlated random variables and one not correlated

I want to compute: $$\mathbb{V}_t \left[ \sum_{i=1}^N \sigma_i \cdot \frac{X_{it}}{Y_t} \cdot Z_{i,t+1} \right]$$ Where $$X_{it}$$ is correlated with $$Y_t$$, and $$Z_{it} \sim N(0,1)$$ uncorrelated random variables. $$\sigma_i$$ is the standard deviation of $$X_{it}$$.