CA MARKOV MODEL

Consider the following sentence: a Markov model tags easilyAssume that based on a  HMM, we have the following probabilities: Emission:P1(a|DET) = 0.1,    P1(easily|ADV) = 0.1,   P1(Markov|N) = 0.1,    P1(model|N)   = 0.095,  P1(model|V)  =0.005, P1(tags|N) = 0.080,  P1(tags|V) = 0.020,Transition probabilities: P(Y|X) Y DET   N   V   ADJ   ADV X DET 0 0.55 0 0.02 0.03   N 0.01 0.1 0.08 0.01 0.02   V 0.16 0.11 0.06 0.08 0.08   ADJ 0.01 0.65 0 0.05 0   ADV 0.08 0.02 0.09 0.04 0.04 Initial probabilitiesP3(DET) = 0.20, P3(N) = 0.06, P3(V) = 0.08, P3(ADV) = 0.07, P3(ADJ) = 0.02.What are the possible tag(s) of the sentence?Assume you want to use the Viterbi algorithm to decode the sentence, write down the expression to be evaluated at the initial step.Write down the expression for the second iteration if the first tag is DET, for a second tag of ADJ

Question 2. [11 Marks]. Consider a Markov process {X(t)}t≥0 with state space S ={0, 1, 2, 3} and Q-matrix, or generator,Q =−q0 2 0 02 −q1 4 00 4 −q2 20 0 1 −q3 .Determine the following quantities.(a) The expected holding time of each state (i.e. the expected amount of time spent in eachstate before a jump).(b) The stationary distribution πQ associated with Q.(c) The proportion of time the process spends in state 3 in the long run.(d) The expected return time, m2 = E2[T2], for state 2.(e) The transition matrix R of the embedded chain.(f) A stationary distribution πR of the embedded chain. Is the stationary distribution πRthat you found unique? Explain your reasoning.2

Explanation of the Markov process and its relevance to mobility modeling.Formulation of the Markovian mobility model.Mathematical representation and equations involved.

. A Markov chain (Xn, n = 0, 1, . . . ) has state space S = {1, 2, 3, 4} and transition matrixP =0 2/5 3/5 01/4 0 1/2 1/40 3/4 0 1/40 0 0 1(a) Draw the transition diagram for this Markov chain. [2 marks](b) Find P (X3 = 1 | X0 = 1, X1 = 2, X2 = 1). [1 mark](c) Find P (X1 = 2, X2 = 1, X3 = 3, X4 = 4 | X0 = 3).

If the initial state probability distribution of Markov chain is ( ) ( )and transition probability matrix of the chain is ( ). Compute theprobability distribution of the chain after 2 steps