@acer 

I don't feel offended.

About OBSERVE, the idea is the following :

I'm working on a course about  probabilities and statistics  for internal purposes within my company. I have decided to construt this course around Maple in order to be able to present formal results and numerical approaches.
This course will begin with the basis, for instance what is a random variable (RV) ? and will present some examples.
My firs idea was to use the Start[Statistics][ContinuousDistributions] application. But I thought it would be smarter to have sliders to instanciate a RV, and to display the values of some of its statistics as thes sliders move.

I then imagined to write this procedure OBSERVE taking as parameter the RV a "student" would like to see.

But youy may be right, I have imagined a too more complex way to do this by passing the distribution as a parameter?

I've solved the issue by rewritting my own "sparsematrixplot" command based on PLOT and textplot (which enables the orientation of text... useful for the column labels that can have several characters and thus superimpose themselves).

 

@epostma 

(reply sent from my professional login)

Thanks for this precision.

@acer 

Thank you acer, I will look to that closely when back home.

@acer 

Thanks for the answer.

I've planned recently to buy a maple 2019 personal license.
Will the compiler be included in the delivery ot will I have to download LLVM by myself?
In addition I've read here that 2019.2 seems to present some problems: what version do you recommend me to buy?

 

@acer 

Just a question: I often meet situations wher simplify(MyExpression) doesn't work. In this cases I try symplify(expand(MyExpression))  and it sometimes works.
I always put this on some "natural", or "normal" difficulty so simplify an expression (the simplified expression may have different form depending on the person): why, do you consider, in the present case, the flaw of simplify merits a bug report?

 

@tomleslie 

Maybe you're right, unfortunately I have no access to Maple for the week to come (this reply from my smartphone). As soon as it will be possible to test your reply I let you know. Be patient.

Thanks in the meantime

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...)