A Continuous Random Packing Problem Consider the interval (0, x) and suppose that we pack in this interval random unit intervalswhose left-hand points are all uniformly distributed over (0, x-1)-as follows. Let the first such random interval be I If I.... I have already been packed in the interval, then the next random unit interval will be packed if it does not intersect any of the intervals I, ..., I, and the interval will be denoted by Ik+ If it does intersect any of the intervals II, .., Ik, we disregard it and look at the next random interval The procedure is continued until there is no more room for additional unit intervals (that is, all the gaps between packed intervals are smaller than 1). Let N(x) denote the number of unit intervals packed in [0, x] by this method. For instance, if x = 5 and the successive random intervals are (5, 1.5), (3 1, 4.1), (4, 5), (1.7, 27), then N(5) = 3 with packing as follows == 0.5 - -12 15 17 27 31 41 Let M(x) =E[N(x)] Show that M satisfies M(x) = 0, x <1, 2