So I'm currently working on a report for homework but I've ran into trouble. Ive been given the fact that: $$\mathbf{t}_i = \mathbf{W}\mathbf{x}_i + {\epsilon}$$

Where $\epsilon \sim \mathcal{N}(0,\sigma^{2}{I})$ (sorry for the non-bold identity matrix, this is taken from my latex).

I'm supposed to evaluate what $p({T} \vert {X},{W})$ is but I'm not used to this since it seems like I'm supposed to evaluate what the likelihood is without having a variance given, I would like to say that:

$p({T} \vert {X},{W},\sigma^{2}I)$ but is this even right, as I said, my examinator wants me to evaluate the expression above, am I missing an important piece of understanding here?


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