Answer Happy

(c) The dynamics of a human organ are studied via a sequence of images over time. In each image, the organ is classified into one of three possible states. The cooccurrence (i.e. transition) counts for a length-1001 sequence of images are recorded as follows (i.e. the (j, k)th element is the count of transitions from state k to state j): C = 150 48 158 108 332 12 99 72 21 Use these statistics to estimate the parameters of a homogeneous Markov chain model for the organ dynamics, and hence evaluate the following: (i) the probability that the organ is in three different states in three successive images; [20%] (ii) the probability that the organ was not in state 3 two images ago, if it is in state 3 in the current image. [25 %]