View source for Poisson race distribution/CalcTable1

{| class="wikitable" border="1" style="min-width:20em;max-width:22em;"
|-
! {{M|k}}
! {{M|X}}
! {{M|Y}}
|-
! rowspan="5" | {{M|0}}
| {{M|X\eq 0}}
| {{M|Y\eq 0}}
|-
| {{M|X\eq 1}}
| {{M|Y\eq 1}}
|-
| {{M|X\eq 2}}
| {{M|Y\eq 2}}
|-
| {{M|\vdots}}
| {{M|\vdots}}
|-
| {{M|X\eq i}}
| {{M|Y\eq i}}
|-
! rowspan="5" | {{M|1}}
| {{M|X\eq 1}}
| {{M|Y\eq 0}}
|-
| {{M|X\eq 2}}
| {{M|Y\eq 1}}
|-
| {{M|X\eq 3}}
| {{M|Y\eq 2}}
|-
| {{M|\vdots}}
| {{M|\vdots}}
|-
| {{M|X\eq i+1}}
| {{M|Y\eq i}}
|-
! rowspan="5" | {{M|2}}
| {{M|X\eq 2}}
| {{M|Y\eq 0}}
|-
| {{M|X\eq 3}}
| {{M|Y\eq 1}}
|-
| {{M|X\eq 4}}
| {{M|Y\eq 2}}
|-
| {{M|\vdots}}
| {{M|\vdots}}
|-
| {{M|X\eq i+2}}
| {{M|Y\eq i}}
|-
| colspan="3" | {{M|\cdots}}
|-
! rowspan="5" | {{M|j}}
| {{M|X\eq j}}
| {{M|Y\eq 0}}
|-
| {{M|X\eq j+1}}
| {{M|Y\eq 1}}
|-
| {{M|X\eq j+2}}
| {{M|Y\eq 2}}
|-
| {{M|\vdots}}
| {{M|\vdots}}
|-
| {{M|X\eq i+j}}
| {{M|Y\eq i}}
|}<noinclude>
This shows why we sum over what we sum over!
</noinclude>