Sahin and Sen (2001) model hourly wind speeds in a northwestern part of Turkey as a Markov chain ()=0,1, with 7 states representing different wind speed levels. Since in python arrays are indexed starting from 0 , let us consider the states to be ={0,1,2,3,4,5,6} with 0 representing the lowest wind speed level etc. The transition matrix is given by =012345600.7560.1740.1410.00300010.1130.8210.001000020.1290.0040.7760.1920.0020030.0020.0010.0820.7530.2270.007040000.0520.7350.3670.053500000.0360.6040.1586000000.0220.789 Implement the transition probability matrix from above as a two dimensional numpy.array(). Compute 250 and list at least two of its rows.

Problem 2 (10 Points) Sahin and Sen (2001) model hourly wind speeds a northwestern part of Turkey as a Markov chain (X)=0,1.... with 7 states representing different wind speed levels. Since in python arrays are indexed starting from 0, let us consider the states to be S = {0,1,2,3,4,5,6} with 0 representing the lowest wind speed level etc. The transition matrix P is given by 4 5 6 0 0 1 0.756 0.113 0.174 0.821 2 3 0.129 0.002 0.004 0.001 0 0 0 0 0 0 2 0.141 0.001 0.776 0.082 0 0 0 P= 3 0.003 0 0 0 0 4 0 0 0.036 0.192 0.753 0.002 0.227 0 0.007 0 0 0.052 0.735 0.367 0.053 5 0 0 0.604 0.022 0.789 6 0 0 0.158 1. Implement the transition probability matrix P from above as a two dimensional numpy.array(). Compute P250 and list at least two of its rows. In [ ]: # WRITE YOUR OWN CODE HERE! FEEL FREE TO INSERT MORE CELLS! # ADD SOME COMMENTS TO YOUR CODE! 2. Compute the stationary distribution a as a right-eigenvector of PT to the eigenvalue 1 (see also Lecture 15, slide 7). In (): # WRITE YOUR OWN CODE HERE! FEEL FREE TO INSERT MORE CELLS! # ADD SOME COMMENTS TO YOUR CODE! # HINT: USE scipy.linalg.eig(..) AND CHECK THE DOCUMENTATION Problem 2 (10 Points) Sahin and Sen (2001) model hourly wind speeds a northwestern part of Turkey as a Markov chain (X)=0,1.... with 7 states representing different wind speed levels. Since in python arrays are indexed starting from 0, let us consider the states to be S = {0,1,2,3,4,5,6} with 0 representing the lowest wind speed level etc. The transition matrix P is given by 4 5 6 0 0 1 0.756 0.113 0.174 0.821 2 3 0.129 0.002 0.004 0.001 0 0 0 0 0 0 2 0.141 0.001 0.776 0.082 0 0 0 P= 3 0.003 0 0 0 0 4 0 0 0.036 0.192 0.753 0.002 0.227 0 0.007 0 0 0.052 0.735 0.367 0.053 5 0 0 0.604 0.022 0.789 6 0 0 0.158 1. Implement the transition probability matrix P from above as a two dimensional numpy.array(). Compute P250 and list at least two of its rows. In [ ]: # WRITE YOUR OWN CODE HERE! FEEL FREE TO INSERT MORE CELLS! # ADD SOME COMMENTS TO YOUR CODE! 2. Compute the stationary distribution a as a right-eigenvector of PT to the eigenvalue 1 (see also Lecture 15, slide 7). In (): # WRITE YOUR OWN CODE HERE! FEEL FREE TO INSERT MORE CELLS! # ADD SOME COMMENTS TO YOUR CODE! # HINT: USE scipy.linalg.eig(..) AND CHECK THE DOCUMENTATION