Python Exercise [10 points total]. Submit two les: 1. explanations, graphics (if any) and results in PDF format with your Python code, and 2. Python Code itself in .ipynb (or .py) format.

Group work policy: You can discuss the problem together with your friends but you have to submit your own work (PDF and Python codes).

(a) [5 points] Read Problem 3.63 about hourly wind speeds in the textbook. The transition probability matrix is given there. Raising the matrix power, obtain the limiting distribution. (problem 3.63 is displayed below)

(b) [5 points] Simulate the chain for 100000 steps and estimate the proportion of times that the chain visits each state.

(10) Python Exercise 10 points total. Submit two files: 1. explanations, graphics (if any) results in PDE format with your Python code, and 2. Python Code itself in ipynb (or py) format. Group work policy: You can discuss the problem together with your friends but you have to submit your own work (PDF and Python codes). (a) [5 points Read Problem 3.63 about hourly wind speeds in the textbook. The transition probability matrix is given there. Raising the matrix power, obtain the limiting distribution. (b) [5 points Simulate the chain for 100000 steps and estimate the proportion of times that the chain visits each state. (10) Python Exercise 10 points total. Submit two files: 1. explanations, graphics (if any) results in PDE format with your Python code, and 2. Python Code itself in ipynb (or py) format. Group work policy: You can discuss the problem together with your friends but you have to submit your own work (PDF and Python codes). (a) [5 points Read Problem 3.63 about hourly wind speeds in the textbook. The transition probability matrix is given there. Raising the matrix power, obtain the limiting distribution. (b) [5 points Simulate the chain for 100000 steps and estimate the proportion of times that the chain visits each state