Equivalence of uniform distribution
Behind a square grid evenly (i.e. uniform distribution) scattered dots.
Could it be considered identical to a sequence of independent events with
probability $\frac{1}{N}$ to hit the cell with dot? And if it so, is it
right to say that the way you choose cells on the grid doesn't matter and
the probability to find the dot would be the same as $\frac{1}{N}$.
How to prove it (or disprove), what the assertions should be involved? And
how to extend the proof on 3-dimensional space and further on
n-dimensions?
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