Let [tex]\{A_i\}[/tex] be independent random variables, real numbers selected uniformly from the interval (0,1-v) for some constant v, 0<v<1.(adsbygoogle = window.adsbygoogle || []).push({});

Let [tex]B_i = \cup^i_{j=1} (A_j,A_j+v)[/tex]

Let [tex]C_i[/tex] be the number of disconnected pieces of [tex]B_i[/tex].

Problem: What is the distribution of [tex]C_i[/tex]? I doubt that a closed form expression is possible but it's tough to even find a computer program to calculate it except via monte carlo.

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# Distribution of Number of Pieces

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