I need clarification on which is the correct way of stating the problem.
Let the collection of pairs $\{(x_i,y_i)\}_{i=1}^n$ be a random sample for a pair $(y; x)$ where $y>0$ and $x$ contains one, that satisfies the conditional density model $$y^{\delta}= x'\beta+e$$ where $e|x\sim \mathcal{N}(0,\sigma^2)$ and $\delta>0$
Show that such a conditional density model is incorrectly posed.
Should it be stated as such:
We know that $y>0$ so $y\in R_{>0}$ But since $e|x\sim \mathcal{N}(0,\sigma^2)$, $e\in R_{\geq 0}$ we have that $(x'\beta+e)\in R_{\geq 0}$
or as such: We know that $y>0$ so $y\in R_{>0}$ But since $e|x\sim \mathcal{N}(0,\sigma^2)$, $e\in R$ we have that $(x'\beta+e)\in R_{\geq 0}$ since the support of normal is on $R$
