Question

You are going to successively flip a coin until the pattern HHT appears; that is until you observe two successive heads followed by a tail. In order to calculate some properties of this game, you set up a Markov Chain with the following states: 0, H, HH, HHT, where 0 represents the starting point, H represents a single observed head on the last flip, HH represents two successive heads on the last two flips, and HHT is the sequence you are looking for. Observe that if you have just tossed a tail, followed by heads, a next toss of a tail effectively starts you over.
a) b)
c) 4. Let Xn be
a) b) c) d)
Please, calculate the transition probability matrix.
Compute the average number of flips in which you have to restart over in the game of flips.
Compute the mean duration of the flips, e.g. the average number of flips until you obtain the desired pattern HHT.

Answer 1