Question on Joint and Conditional densities in Probability

Problem 3. (Review from 420: Joint and conditional densities) Suppose Z is a standard normal random variable, so Z has expectation zero and variance 1. A X2 random variable with 1; degrees of freedom is a gamma-distributed random variable with parameters with parameters cu = 12/2, A = 1/2. Suppose V is a x2 random variable with 1/ degrees of freedom that is independent of Z. Dene U by U = Z \"EV/v - a) Compute the conditional density fw'vl't") of U given V = o. b) Find the joint density f(u,1:) of the pair U, V. c) Use the previous part to obtain the density of U