Spacing Distribution of a Bernoulli Sampled Sequence
classification
🧮 math.PR
keywords
distributionfracbernoullisequencespacingspacingsclosedconverge
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We investigate the spacing distribution of sequence \[S_n=\left\{0,\frac{1}{n},\frac{2}{n},\dots,\frac{n-1}{n},1\right\}\] after Bernoulli sampling. We describe the closed form expression of the probability mass function of the spacings, and show that the spacings converge in distribution to a geometric random variable.
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