Show transcribed image text Q.2 A mouse travels in a maze (shown in figure). At each discrete time-step, the mouse chooses one of the doors from the room it is curently in (uniformly at random), and moves to the chosen neighboring room Room three has a block of cheese in it (reward for the mouse (a). Model the location of mouse as a DTMC. Is it irreducible and aperiodic? Justify your answers. b). Write the one-step probability transition matrix (c). Find the steady state distribution Ï€ for this DTMC. 4 cheese Figure 1: The maze. nand Î£ (The steady state distribution is defined as a row vector Ï€ of probabilities such that Ï€ 1 where P is the one-step transition matrix and n is the number of states.) Ï€

Q.2 A mouse travels in a maze (shown in figure). At each discrete time-step, the mouse chooses one of the doors from the room it is curently in (uniformly at random), and moves to the chosen neighboring room Room three has a block of cheese in it (reward for the mouse (a). Model the location of mouse as a DTMC. Is it irreducible and aperiodic? Justify your answers. b). Write the one-step probability transition matrix (c). Find the steady state distribution Ï€ for this DTMC. 4 cheese Figure 1: The maze. nand Î£ (The steady state distribution is defined as a row vector Ï€ of probabilities such that Ï€ 1 where P is the one-step transition matrix and n is the number of states.) Ï€