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problem 1: Use any libraries on Matlab to build the HMM model that includes two hidden states (A, B) and two possible events in observation (yes, no):

a) Initial probabilities of each state:  p(A) = 0.32, p(B) = 0.68

b) Transition probability matrix (between the hidden states):

2090_transition probability matrix.jpg

c) observation probability matrix (the probability of observing some event for specific hidden state):

377_hidden state.jpg

Find log likelihood for the given two sequences of observations: 'yes, yes, no, yes, no, yes, yes' and 'no, no, no, yes, no, yes, yes'. Sketch a diagram of HMM model with probabilities for given sequences of the observations.

problem 2: Use any library on Matlab that contains implementation of Simulated Annealing to find minima in the following optimization problem: z=abs(atan((x^2+y^2 -sin(x)))). Use available implementation of the Genetic Algorithm for the same problem. What are the coordinates of found minima? Which set of parameters does provide better convergence for used methods?

prepare a report that includes plot of the function to be optimized.

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