Suppose the distribution of Y, conditional on X = x is n(x,x 2 ) and that the marginal distribution of X is uniform(0,1). Prove that Y/X and X are independent. The solutions manual says that the...

Suppose the distribution of Y, conditional on X = x is n(x,x²) and that the marginal distribution of X is uniform(0,1).

Prove that Y/X and X are independent.

The solutions manual says that the bivariate transformation t = y/x, u = x will also show that the joint density factors.