4. Jump Up, Fall Down

Consider a Markov Chain with state space0,1,2,...,12and transition behavior given by:

• For011 , the distribution of+1given=is uniform on+1,+2,...,12 .
• (12,0)=1 .

a)Complete the cell below to construct the transition matrix of this chain and assign it to the namejump_fall.

#Answer to 4a  s = np.arange(...) def transition_probs(i, j): ... jump_fall_tbl = Table().... jump_fall = jump_fall_tbl... jump_fall 

b)Explain why this chain is irreducible and aperiodic.

c)Write code that usesjump_fallandprob140methods so that the final line evaluates to the expected long run proportion of time the chain spends at 0.

#Answer to 4c ...