3.4.4 A coin is tossed repeatedly until two successive heads appear. Find the mean number of tosses required. Hint: Let $X_{n} $ be the cumulative number of successive heads. The state space is $0,1,2$, and the transition probability matrix is $$ P=1\left(\begin{array}{ccc} 0 & 1 & 2 0 & \frac{1}{2} & \frac{1}{2} &0 \frac{1}{2} & 0& \frac{1}{2} \ 2 & 0& 0 & 1 \end{array} ight. $$ Determine the mean time to reach state 2 starting from state 0 by invoking a first step analysis. SP.SS.379