Thanks, Rober.

Actually, the question was raised by a student who is taking the introductory course on statisitcs. I wish Maple may improve its documentation of Sample, Distribution and RandomVariable commands by addressing similar issue/limitations encountered in this post. Though I understand this might have to unfold much deeper concepts, it should reduce the beginners' frustration and facilitate their learning.

Yes. I meant the outline. I will use textplot.

Thank you for your detailed explanation. And the last commands are what I was looking for.

However, your answer actually activated the other more fundalmental/interesting question: we should always specify the data type, discrete or continous, for drawing histogram Or how to handle this without the ex-ante knowledge of data type?

This data is originally discrete (say by design). Without knowing it, Maple's default treatment is kind of "continuous" approximatation. I guess Maple somehow approximate the discontinuous CDF of discrete data. Then it draws a "PDF plot" representation for a histogram of discrete data/random variable.  Unfortunately, in this case, this approximation is weird. And basically, it is wrong for the case of discrete random variable. But, I still appreciate this "mistake" which drives me to digest the deeper concept.

Then, this draws back to the question raised above. Actually, I tried this data in the other statistic software. Its default mode is always to implicitly add some "bincount". This seems always right in terms of the definition of histogram no matter what type the data is. Probably this is the best workaround.

By my experience (though very short) about the Statistics package, it has weakness in discrete cases. For instance, it does not has a command like "PMF" (probability mass function). ProbabilityDensityFunction and ProbabilityFunction seems always keep a "continuous" mind in treating all objects (sorry I don't have an example right at hand). Plus, Distribution command cannot work in a discrete case (there was a post just recently about this and Prof. Robert Isreal sent a request already). Let me know if this inference about your algorithm or my understanding is wrong. Thanks.

Alejandro: Thanks for the response.

But these methods don't make difference in my case. I have to acknowledge, based on the history of playing maple, it is really a matter of experience. Thanks anyway.

Alejandro and Robert: Your help and advise are highly appreciated.

I recall there seems some methods to force maple to solve symbolically under real domain.  What are they?

Is there good documentation to read about how Maple understands the expression for its solve command? Hence, we can learn how to "prepare" the target well.