On the One Dimensional Poisson Random Geometric Graph

<table>Illustration of the condition equivalent to <svg height="14.625" id="M163" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 42.099998 14.625" width="42.099998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.625)">
<g transform="translate(72,-60.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛽</tspan>
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<text transform="matrix(1,0,0,-1,-64.97,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
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<text transform="matrix(1,0,0,-1,-56.63,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">≥</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">𝑛</tspan>
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Journal of Probability and Statistics

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Figure 3

Figure 3: On the One Dimensional Poisson Random Geometric Graph 