It may seem a simple question for you, but it's driving me crazy. Given the regression model $z = wx + \epsilon$, where $ \epsilon \sim \mathcal{N} (0, (\sigma x)^{2} $, $ z \sim \mathcal{N}(wx, \sigma^2 x^2) $, and the value of $\sigma$ assumed to be known.
What is the distribution of $z/x$ given $x$ ?
Maybe I'm missing something. I opted for a change of variable, such that $y = z/x$ and I tried to model the probability of $p(y|x)$, but I just got lost in my computations.
Any idea?
If you want $\frac {z} {x} | x$, you can consider $x$ as known, as a constant. Then, for the properties of the normal distribution, $ \frac {z} {x} | x \sim N(\frac{wx}{x}, \frac{\sigma^2 x^2}{x^2})=N(w,\sigma^2)$.
Please, check my reasoning, but I think that it is like this.