Gaussian Bayes Classification:
two classes: $y \in \{-1,+1\}$
Dependencies for a vector of features ($x_1,x_2,x_3)$: $x_1=z,x_2=2z,x_3=t+3$, where
$$P(z\mid y=+1) = \aleph(z;\mu_+,1),\qquad P(z\mid y=-1) = \aleph(z;\mu_-,1)$$
$$P(t\mid y=+1) = \aleph(t;\nu_+,1), \qquad P(t\mid y=-1) = \aleph(t;\nu_-,1)$$
$z$ and $t$ are conditionally independent given $y$.
Prior: $P(y=+1) = P(y= -1) = 0.5$
What is the likelihood $p(x_1,x_2,x_3\mid y) $ for each $y$?