# Define a problem using chernoff bounds

We are preparing this for an exam.

Given the division of a plane into a number of regions of different sizes. We would like to find, or guess, which is the biggest region, by doing the following.

We will shoot a number of random points at the plane, and then conclude that the region containing the most points, is also the biggest.

The question is: how do use Chernoff bounds to say how many random points we need to shoot, to know that we have found the biggest region with, say, 75% probability?

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What parameters is the number of points allowed to depend on? Consider two regions of size $1$ and $1+\epsilon$, with $\epsilon$ small. We would need to shoot many points to distinguish which is biggest with 75% probability. – Colin McQuillan Jan 3 '13 at 21:35
There is no restriction on what parameters the points depend on. It could be arbitrarily few or many. Your problem statement is good. The question is, how do we answer/represent it using Chernoff? – andershqst Jan 4 '13 at 8:57