USE MATLAB.

Part 1 Suppose we have a Markov Model (states are s1, s2 and s3) with transition matrix defined as follow: 1/3 23 0 0 2/3 1/3 What is the probability of P(s1sz which refers to given the system is in state s3 when t0 what is the probability of end up being in state si when t 2? (two steps transition) What is the probability of P(sility of Ps901s and probability of Ps00)1 write a function that takes the transition matrix A, initial state so, transition steps t and final state St, return the probability of P(s I s) For example, in the above setup, the function input should be transition matrix A, initial state so 2, transition steps 100, final state s,0 and output should be around 0.2 (P(s10 1 50)) (10)0 Part 2 Suppose we have a Hidden Markov Model (states are si, S2 and s3 and observations are o1 and 02) with transition matrix A and emission matrix B defined as follow: 1/3 2/3 0 0 0 2/3 1/3 A-113 2/3|; B-11/109/10 1/2 1/2 What is the probability of Po),0),02 1) where s1 represents the first state ad means that then system is in the first state at t0. In other words, what is the probability of observing a sequence of observations O [o1, 02, 02] when t 1,2 and 3 respectively? Write a function that takes A, B, I and O and outputs the probability of Po,.0%1s). For example, in the above setup, the input should be A, B, I [1,0, 0], and O [0,1,1] Part 1 Suppose we have a Markov Model (states are s1, s2 and s3) with transition matrix defined as follow: 1/3 23 0 0 2/3 1/3 What is the probability of P(s1sz which refers to given the system is in state s3 when t0 what is the probability of end up being in state si when t 2? (two steps transition) What is the probability of P(sility of Ps901s and probability of Ps00)1 write a function that takes the transition matrix A, initial state so, transition steps t and final state St, return the probability of P(s I s) For example, in the above setup, the function input should be transition matrix A, initial state so 2, transition steps 100, final state s,0 and output should be around 0.2 (P(s10 1 50)) (10)0 Part 2 Suppose we have a Hidden Markov Model (states are si, S2 and s3 and observations are o1 and 02) with transition matrix A and emission matrix B defined as follow: 1/3 2/3 0 0 0 2/3 1/3 A-113 2/3|; B-11/109/10 1/2 1/2 What is the probability of Po),0),02 1) where s1 represents the first state ad means that then system is in the first state at t0. In other words, what is the probability of observing a sequence of observations O [o1, 02, 02] when t 1,2 and 3 respectively? Write a function that takes A, B, I and O and outputs the probability of Po,.0%1s). For example, in the above setup, the input should be A, B, I [1,0, 0], and O [0,1,1]