Let $X_1 \in \text{Gaussian}(\mu_1, \sigma^2_1), \ldots, X_N \in \text{Gaussian}(\mu_N, \sigma^2_N)$ each be a D210: Gaussian random real number such that

(i)	$X_1, \ldots, X_N$ is an D3842: Uncorrelated random collection

Then \begin{equation} \sum_{n = 1}^N X_n \overset{d}{=} \text{Gaussian} \left( \sum_{n = 1}^N \mu_n, \sum_{n = 1}^N \sigma^2_n \right) \end{equation}