The transition matrix is 4 7 1 (0.756 0.113 0.129 0.0020 2 0.174 0.821 0.004 0.001 0 3 0.141 0.001 0.776 0.082 0 0 0 0 0 0 0 0.002 0.227 0.735 0.0360 P=4 0.003 0 0.192 0.753 0.052 0 60 00.007 0.367 0.604 0.022 0 0.053 0.158 0.789 (a) Find the limiting distribution by (i) taking high matrix powers, and (ii) using the stationary command in the utilities.R file. How often does the highest wind speed occur? How often does the lowest speed occur? (b) Simulate the chain for 100,000 steps and estimate the proportion of times that the chain visits each state. The transition matrix is 4 7 1 (0.756 0.113 0.129 0.0020 2 0.174 0.821 0.004 0.001 0 3 0.141 0.001 0.776 0.082 0 0 0 0 0 0 0 0.002 0.227 0.735 0.0360 P=4 0.003 0 0.192 0.753 0.052 0 60 00.007 0.367 0.604 0.022 0 0.053 0.158 0.789 (a) Find the limiting distribution by (i) taking high matrix powers, and (ii) using the stationary command in the utilities.R file. How often does the highest wind speed occur? How often does the lowest speed occur? (b) Simulate the chain for 100,000 steps and estimate the proportion of times that the chain visits each state