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within the probability distribution of p(y|x,w,c,d,a) c and d are implicitly defined within f(x). For a) I would have suggested:

p(y | x,w,c,d,a) = N(y | f(x),a)

My question: Is it okay to ignore c,d in the N-(Gaussian) expression?

And if so, concerning b): Is it correct that the expression p(t|x,w,c,d,a) = N(t | f(x),a)

so it's simply the same as we had before since y tries to approach t?