1. The discrete random variables Xo, X, and X have the following joint distribution: For Xo = 2: X 2 4 6 1 X 3 5 30 60 60 20 T 60 60 20 For Xo = 5: X 2 4 6 1 18 1 18 X1 3 2010 5 36 36 36 36 where the left table is the joint pmf values of the random vector X (Xo, X1, X) for Xo = 2, and the right table is the joint pmf values of X for Xo = 5. Answer the following questions. All logarithms are in base 2. If you choose to write a script to compute the answers, make sure to attach your code, but also write the answers. If you choose to hand-write your answer justify all your solutions. 1c) Which, if any, of the pairs (X, X2), (Xo, X2), and (Xo, X) are inde- pendent? Justify your answer. 1d) What is the conditional distribution of the random vector (X1, X2) given Xo = 2? Repeat for given Xo = 5. le) Are the random variables X and X2 conditionally independent given Xo = 2? = 2? Repeat for given Xo = 5. 1f) What is the conditional distribution of X given Xo = 5 and X = 2?