Poisson race distribution/CalcTable1
From Maths
[ilmath]k[/ilmath] | [ilmath]X[/ilmath] | [ilmath]Y[/ilmath] |
---|---|---|
[ilmath]0[/ilmath] | [ilmath]X\eq 0[/ilmath] | [ilmath]Y\eq 0[/ilmath] |
[ilmath]X\eq 1[/ilmath] | [ilmath]Y\eq 1[/ilmath] | |
[ilmath]X\eq 2[/ilmath] | [ilmath]Y\eq 2[/ilmath] | |
[ilmath]\vdots[/ilmath] | [ilmath]\vdots[/ilmath] | |
[ilmath]X\eq i[/ilmath] | [ilmath]Y\eq i[/ilmath] | |
[ilmath]1[/ilmath] | [ilmath]X\eq 1[/ilmath] | [ilmath]Y\eq 0[/ilmath] |
[ilmath]X\eq 2[/ilmath] | [ilmath]Y\eq 1[/ilmath] | |
[ilmath]X\eq 3[/ilmath] | [ilmath]Y\eq 2[/ilmath] | |
[ilmath]\vdots[/ilmath] | [ilmath]\vdots[/ilmath] | |
[ilmath]X\eq i+1[/ilmath] | [ilmath]Y\eq i[/ilmath] | |
[ilmath]2[/ilmath] | [ilmath]X\eq 2[/ilmath] | [ilmath]Y\eq 0[/ilmath] |
[ilmath]X\eq 3[/ilmath] | [ilmath]Y\eq 1[/ilmath] | |
[ilmath]X\eq 4[/ilmath] | [ilmath]Y\eq 2[/ilmath] | |
[ilmath]\vdots[/ilmath] | [ilmath]\vdots[/ilmath] | |
[ilmath]X\eq i+2[/ilmath] | [ilmath]Y\eq i[/ilmath] | |
[ilmath]\cdots[/ilmath] | ||
[ilmath]j[/ilmath] | [ilmath]X\eq j[/ilmath] | [ilmath]Y\eq 0[/ilmath] |
[ilmath]X\eq j+1[/ilmath] | [ilmath]Y\eq 1[/ilmath] | |
[ilmath]X\eq j+2[/ilmath] | [ilmath]Y\eq 2[/ilmath] | |
[ilmath]\vdots[/ilmath] | [ilmath]\vdots[/ilmath] | |
[ilmath]X\eq i+j[/ilmath] | [ilmath]Y\eq i[/ilmath] |
This shows why we sum over what we sum over!