If \( f(x) \) and \( g(y) \) are non-negative functions such that \( \int_{-\infty}^{\infty} f(x) d x=\int_{-\infty}^{\infty} g(y) d y=1 \), let the pair of continuously distributed random variables have p.d.f. given by \( f_{X, Y}(x, y)=f(x) g(y) \). a) Find the marginal distributions of \( X \) and \( Y \); b) Find the conditional distribution of \( X \) given that \( Y=y \); and the conditional distribution of \( Y \) given that \( X=x \) c) Explain why the answers in parts a) and b) are unsurprising.