Please answer the following question with steps, thank you

Random variables X, Y, Z are said to form a Markov chain in that order (denoted by X - Y - Z) if their joint probability distribution can be written as: p(X, Y, Z) = p(X) . p(Y[X) . p(Z|Y) I. Suppose (X, Y, Z) forms a Markov chain. Is it possible for I (X; Y) = I(X; Z)? If yes, give an example of X, Y, Z where this happens. If no, explain why not. [4 Marks] II. Suppose (X, Y, Z) does not form a Markov chain. Is it possible for 1 (X; Y) 2 1(X; Z)? If yes, give an example of X, Y, Z where this happens. If no, explain why not. . [4 Marks] III. If X - Y - Z then show that [6 Marks] . I(X; Z)