Let $X_1, \ldots, X_N \in \text{Random}(\mathbb{R})$ each be a D3161: Random real number such that

(i)	$X_1, \ldots, X_N$ is an D2713: Independent random collection

Let $\alpha_1, \beta_1, \ldots, \alpha_N, \beta_N \in \mathbb{R}$ each be a D3161: Random real number such that

(i)	\begin{equation} \alpha_1 \neq 0, \quad \ldots, \quad \alpha_N \neq 0 \end{equation}

Then $\alpha_1 X_1 + \beta_1, \quad \ldots, \quad \alpha_N X_N + \beta_N$ is an D2713: Independent random collection.