I was wondering... Is there any formula for a two dimensional discrete uniform distribution? I've googled a little bit but I don't seem to find anything... I hope that somebody can help!
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I assume you have an $m \times n$ grid of points and you want a PMF (probability mass function) which gives the probability of drawing a certain point. Since you have $m\cdot n$ points in total and you want the mass function to be uniform that means for each $i \in \{1,\dots,m \}$ and $j \in \{1,\dots,n \}$,
$$ P(X = x_{i,j}) = \frac{1}{m \cdot n}. $$
