1. Suppose X and Y are jointly continuous random variables with frix(y, x) = rexp(-yr)/(y > 0) and fx(I) = exp(-r)I(x > 0). (a) Based only on the information given in the question, without making any additional calculations, determine whether X and Y are independent. (b) Find the marginal density of Y. (c) Find the conditional density of X given Y and, if it corresponds to a known distribution, state its name