Is This The Proper Way to Use Observed RVs of Different Lengths?

Not sure I understand your use case of “observed parameters ”. The code is fine but it will be the same as if you are doing:

Thank you for the reply. So in the above case, the Normal distribution isn’t being used at all? I want to setup a linear model:

z = \alpha + Y \cdot \beta^T where Y is, for example, 2 Normal distributions (containing different length observations).

I.e. [\mathcal{N}_0, \mathcal{N}_1] \cdot [\beta_0, \beta_1]^T.