Unformatted text preview: (a) P [ X 1 = 1  X = 0 ,X 2 = 1] (b) P [ X = X 1 ] (c) P [ X 1 6 = X 2 ] 4. Consider a sequence of independent tosses of a coin with probability of heads, p . Let X n be the total number of tosses which yielded a heads given n tosses. (a) Verify that X n is a Markov Chain. Explicitly note the state space. (b) Determine the transition probability matrix. Is the Markov Chain homogeneous or nonhomogeneous. (c) Repeat (a) and (b) if X n is deﬁned as the total number of tosses which yielded heads minus the total number of tosses which yielded tails given n tosses....
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 Spring '06
 Caire
 Gate, Probability theory, Markov chain, discrete time Markov, discretetime Markov chain, i.i.d. sequence Xn

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