The problem is not well posed.

Without restriction on the diameters d[m] of the new balls every points in D = C \ B(X1, R1) meets your requirement if d[m] --> 0⁺.

More of this, as N --> +infinity the probability that any point of  radius < 1 meets the requirements goes to 1.
This because the ratio V / 2^N of the volume of B(X1, R1)  to the volume of C goes uiformily to 0 as N increases
(V = pi^(N/2) * R1^N / Gamma(N/2+1)).

 

@acer

Thanks (PS: it works in Maple 2018 too)

@acer 

Letting a point free is a very good idea to try understanding how the algorithm works: I'm going to execute your little code of yours.
You wrote " Visually the behavior "makes sense", but what is the precise characterization in words?": right the way Maple fills non simple polygons make sense, at least visually. As it is easy to fill simple polygons in a non ambiguous way (because their interior does exist), it's not the case for non simple polygons.
Other common methods are based on drawing (for instance horizontal) parallel lines and swithing between "coloring" and "non coloring"  as soon as these lines cut a side of the polygon.
But if you use this latter for the stellate pentagon
a := evalf(2*Pi/5):
p := [ seq([cos(a*k), sin(a*k)], k in [1, 3, 5, 2, 4]) ]
PLOT(POLYGONS(p));
then a central regular pentagon should be kept white as it is colored. Probably it is what the intuition suggests, but it doesn't help to understanf the coloring algorithm Maple uses.

I implemented different ways to color general polygons and none of them offer the same appearance than Maple's does.
But maybe it's a vain quest for the interior of a non simple polygon is not defined?

@ThU 

Thank you.
There are indeed impressive new drawing options in Maple 2019.
For now on I have at best Maple 2018.

@Thomas Richard 

Thank you Richard.

To answer your last phrase I'm working on a coupling between Maple and R to delegate the latter some specific calculations which would be too complex to recode in Maple. The R code generated in Maple is saved in a text file "MyFile.R"   that must me made executable before launching the command ssystem("..../bin/Rscript MyFile.R").

 

@Carl Love 

You're right, I'd forgotten ths Welch's test and its "equivalent" number of degrees of freedom.
Your argument is undisputable.
Consider my question as null and void

@Carl Love 

I will rectify this as soon as I get home.

@Carl Love 

Right, once I sent my answer, I realized that I should have mentioned that the constructor || makes the variable global (something that caused me serious problems the first time I used this in a procedure...)
 

@Thomas Richard 

Thanks for your quick reply, here is a toy problem:

Toy_Problem.mw

@vv 

sorry for this late answer...

Thanks you vv

@dharr 

I do not have Maple 2017.
In Maple 2018.0, Windows 7 version, ID 1298750, using names returns an explicit error saying that strings are expected.

Maybe a slight change from one version to the next one...

@Carl Love @vv

You're 100% right.
I redid the exercice this morning, mind calm , and I clearly fooled myself yesterday.
I think it's not appropriate to chat on mapleprimes while watching a soccer's game

@tomleslie 

which is a real pity for loops are very common in probabilistic graphical models.
Of course you can always cheat by writting {1, x}, {x, 1} instead of {1, 1} and give ad hoc transitions probabilities to simulate a 1 to 1 transition, but it would not be smart at all.
Let me immediately moderate these comments: what is really intersting from a practical point of view is the transition matrix (which could be the adjencicy matrix in a zero-loop graph)... indeed, the graph here is more an educational suport than a computational tool.

@acer 

Now from the office...

Worksheet Tab3.mw, after a few personal modifications, works perfectly well.

Thank you very much acer

@Carl Love 

If you write sol := dsolve(...), isn't it the value of sol('numfun')  ?