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Perfect Samples

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Parts

Part 1

Assume that you are taking samples of size $s$ from a population. For each sample, let $p$ represent the probability that every point in that sample is an inlier and let $e$ represent the proportion of points in the sample that are outliers. Derive an equation in terms of $s$, $p$ and $e$, to calculate the number of samples ($N$) needed in order to be 99% confident that there it at least one sample drawn that contains no outliers.