Exercise 1.4 Show that the function f (y) given above is the density of Y when Y N(,V) and V is nonsingular. Hint: If

Exercise 1.4 Show that the function f (y) given above is the density of Y when Y ∼ N(μ,V) and V is nonsingular.

Hint: If Z has density fZ(z) and Y = G(Z), the density of Y is fY (y) = fZ(G−1(y))|det(dG−1)|, where dG−1 is the derivative (matrix of partial derivatives) of G−1 evaluated at y.