The age of a mobile phone is measured in months, and fractions of a month do not count. If a mobile phone is burned out during the month, then it is replaced by a new one at the beginning of the next month. Assume that a mobile phone that is in a working condition at the beginning of the month, possibly one that has just been bought, has probability p = 0.9 of surviving at least one month so that its age will be increased by 1. Assume also that the successive mobile phones used lead independent lives. Let X0 = 0 and Xn denote the age of the mobile phone that is being used at the beginning of the (n + 1)-st month. (We begin with the first month, thus X1 = 1 or 0 depending on whether the initial mobile phone is still in working condition or not at the beginning of the second month.) The process {Xn} n=0 is an example of a renewal process. Show that it is a recurrent Markov chain, find its transition probabilities and stationary distribution. Note: The life span of a mobile phone being essentially a continuous variable, a lot of words are needed to describe the scheme accurately in discrete time, and certain ambiguities must be resolved by common sense. It would be simpler and clearer to formulate the problem in terms of heads and tails in coin tossing (how?), but then it would have lost the flavor of application!