Michelle will ?ip a coin until she gets heads four times in a row. De?ne X0=0 and, for n>=1, Xn=the number of heads in the current streak of heads after the nth ?ip. (a) If the ?rst seven ?ips result...

Michelle will ?ip a coin until she gets heads four times in a row. De?ne X0=0 and, for n>=1, Xn=the number of heads in the current streak of heads after the nth ?ip. (a) If the ?rst seven ?ips result in the sequence HTHHHTH, determine the values of X1, X2, ... , X7.[Hint: Each time Michelle ?ips tails, the streak is reset to 0.] (b) Is this an example of a Markov chain? Explain why or why not. (c) Identify the state space of the chain. Treat reaching four heads in a row in the same manner that the $3 state was treated in the Gambler’s Ruin scenario of Example 6.2. (d) Assume P(H)=p for this particular coin. Determine the one-step transition probabilities of this chain, and draw the corresponding state diagram.