: Let (X, r≥ 1} be the integer-valued identically distributed intervals between the times of a recurrent event process. Let L be the earliest time by which there has been an interval of length a containing no occurrence time. Show that, for integral a, E(s) = saP(X₁ > a) 1-1 s² P(X₁ =r)*

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Let (X, r≥ 1} be the integer-valued identically distributed intervals
between the times of a recurrent event process. Let L be the earliest time by which there has been an
interval of length a containing no occurrence time. Show that, for integral a,
E(s) =
saP(X₁ > a)
1-₁ s² P(X₁ =r)*
Transcribed Image Text:: Let (X, r≥ 1} be the integer-valued identically distributed intervals between the times of a recurrent event process. Let L be the earliest time by which there has been an interval of length a containing no occurrence time. Show that, for integral a, E(s) = saP(X₁ > a) 1-₁ s² P(X₁ =r)*
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