Consider a sequece of iid random variables { n , n = 0 , 1 , 2 , ... } with mass probabilities P ( n = 0 ) = 0.2 , P ( n = 1 ) = 0.3 , and P ( n = 2 ) = 0.5 . Define a Markov chain ( X n ) n 0 on the state space S = { 0 , 1 , 2 } using the rule X n = ( X n 1 + n ) m o d 3 , where a m o d b denotes the reminder upon division of a by b . Write the transition matrix for this Markov chain