1. The problem statement, all variables and given/known data Consider f = wT x, where p(w) ∼ N (w|0, Σ). Show that p(f|x) is Gaussian. 3. The attempt at a solution So there are apparently two approaches to this problem using either the linearity of f in terms of w or moment generating functions. But I'm having a lot of trouble figuring out how to proceed. I can see the we can use the moment generating function to show that the sum of two independent normal distributions is also a normal distribution (i.e since the sum can be written as a product of the mgf's). But I'm a bit stumbled by this. Any help is appreciated. Edit: we are allowed to assume that the variables of w (w1, ...wd) are independent.