How to solve 3a-3d

2. Prove Theorem 17.2. 3. Let X. Y and Z have the following joint distribution: Y=0 Y=1 Y=0 Y=1 X=0 .405 .045 X=0 125 .125 X =1 .045 005 X =1 125 .125 Z =0 7 -1 (a) Find the conditional distribution of X and Y given Z = 0 and the conditional distribution of X and Y given Z - 1. (b) Show that X II Y Z. (c) Find the marginal distribution of X and Y. (d) Show that X and Y are not marginally independent