Build probability estimates from the sampling mechanism, distinguish events from counts, and turn average waiting times into carefully justified deadline bounds.
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Collision indicators and collection stages need a justified sampling mechanism but expectation addition has broader validity.
No. Linearity holds for finite sums with finite expectations. Independence is a separate hypothesis used to derive the probabilities of the component events or waiting times.
Collection time connects waiting stages to the reciprocal sum.
For positive integers N, ln(N+1) ≤ H_N ≤ 1+ln N. These bounds explain logarithmic growth without making a finite mean a guaranteed deadline.
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Audit the sampling mechanism and its guarantees
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Count repeated labels exactly, distinguish collision counts from collision events, and certify a controlled exponential approximation.
6 practice tasks.
Derive expected collection time and deadline bounds while tracking the assumptions behind uniform sampling.
6 practice tasks.
