consider a Hidden Markov Models (HMMs) where the chain St at a time t is in of three possible states st = A, B, C. The transition matrix of this HMM shall be given by

T=f(A,B,C)=1AB/2C/2A/21BCV/2A/2B/21C=0.640.3150.140.180.370.140.180.3150.72

Indicate for each of the following statements if it is true or false

a) The row vector = (0.35, 0.2, 0.45) is a stationary distribution of this Markov Chain

b) The Markov Chain is periodic

c) Any stationary distribution for this Markov chain is also a stationary distribution for a Markov chain with transition matrix T' = =f(A,B,C) .

d) For this chain, P(S2=AS0)<P(S2=BS0=A)

e) The probability P(S1=A,S2=AS0=A,T)=0.4096