In the following questions, assume that the mathematical model of an MDP(S,A,ps,r,) is given in the following form. - State set S is represented by integers S={1,,n}, - Action set A is represented by integers A={1,,m}, - State transition probabilities ps are given by a 3D array P in the form pijk=ps(sjsi,ak), - Rewards r are given by a 3D array R in the form rijk=r(si,sj,ak). Note that since the sets S and R are composed of consecutive integers starting from 1, it is enough to known m and n to define these sets. m and n can be easily obtained from the dimensions of the matrix P or R. 1) Consider a finite horizon MPD(S,A,ps,r,1) with the final time T. a) Write a MATLAB function that takes arrays P,R, and the horizon T corresponding to the finite horizon MDP and computes the optimal value function and policy of this MDP. The function should return two values. One is a 2D matrix V composed of the elements vit of the time-dependent optimal value function computed. The other is PI composed of the elements of the time-dependent optimal policy it computed. b) Find the optimal value function and policy of the Stochastic Roller problem studied in the class for T=10 using the function you wrote in part a). Note that you should represent the states L,M,H, and the actions spin and don't spin using integers