1.29 Uniform density over a union of two square regions Let the random vari- ables X and Y be jointly uniformly distributed on the region {0 u 1,0 v 1} U {1 u < 0, 1 v < 0}. (a) Determine the value of fxy on the region shown. (b) Find fx, the marginal pdf of X. (c) Find the conditional pdf of Y given that X = a, for 0 < a 1. (d) Find the conditional pdf of Y given that X = a, for 1 a < 0. (e) Find E[Y|X = a] for |a| 1. (f) What is the correlation coefficient of X and Y? (g) Are X and Y independent? (h) What is the pdf of Z = X +Y?