2. Each toss of a coin results in heads with probability p (> 0). If m(r ) is the mean number of tosses up to and including the r th head, show that m(r ) = p



1 + m(r − 1)



+ (1 − p)



1 + m(r )



for r = 1, 2, . . . , with the convention that m(0) = 0. Solve this difference equation by the method described in Appendix B.