Suppose that X and Y are independent standard normal variables. Let Z = Y/X. Find the density of Z by following these steps: (a) Write P(Z z, X > 0) as a double integral using the joint density of X and Y . (b) Write P(Z z, X < 0) as a double integral using the joint density of X and Y . (c) What is P(Z z, X = 0)? (d) Give a formula for the cdf of Z in terms of these 3 answers. (e) Find the derivative of the previous part to compute the density of Z. (f) If necessary simplify the answer to eliminate any remaining integrals.