Exercise 3.10 In contrast to Exercise 3.9, suppose that X N(0, 2), but Y depends on

Exercise 3.10 In contrast to Exercise 3.9, suppose that X ∼ N(0, σ2), but Y depends on the realization of X. Namely, suppose that Y ∼ N(μ(x), σ2(x))

given X = x, x ∈ IR, for some functions μ(x) and σ2(x) > 0. Obtain the density function of Z = X + Y .