P(X = x | Y = y) = 0 for x < y.

Otherwise, though...

... this example is for N = 3, using the same approach as here, http://www.mathhelpforum.com/math-he...on-169035.html.

The first stage gives the branches a weighting of 6, i.e. 3!, a common multiple of all the possible x's.

The second stage shares that weight between x possible y's.

So for example, P(X = 2 | Y = 2) = 3/5, while P(X = 3 | Y = 2) = 2/5. (Try to use the tree to see why that is.)

For P(X = x | Y = y) I guess you can then make a general numerator of

... and a denominator of

Hope this isn't too far off...

__________________________________________________ ____________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!