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Is it possible to see the step-by-step calculation done by TransformProduct function in MathStatica package?

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    $\begingroup$ I'm voting to close this question as off-topic because this is not a question about Mathematic per se, but for a third-party package/application. I suggest using their support fora/staff for such questions at the package/application web site. $\endgroup$
    – ciao
    Mar 11, 2017 at 2:26
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    $\begingroup$ I think the above comment seems confused. First, packages are part of the inherent design and structure of Mathematica itself, and its generality to cover wider or more specific areas. Second, the discussion of Mma packages lies fully within the remit of the mathematica.SE site, which is why there is a packages tag with over 450 postings attributed to same. Do you also want to shut down all questions about Combinatorica,or the Groebner basis packages, or the dozens of Wolfram add-on packages, etc? $\endgroup$
    – wolfies
    Mar 11, 2017 at 14:16
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    $\begingroup$ I have voted to re-open this question which is plainly about a Mathematica package, and so about Mathematica. More generally, this is an interesting topic for discussion/meta-- namely whether Mathematica packages are in fact Off Topic for the Mathematica SE site: referred to meta --- meta.mathematica.stackexchange.com/questions/2109/… $\endgroup$
    – wolfies
    Mar 11, 2017 at 16:50
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    $\begingroup$ @ciao :"I suggest using their support fora/staff for such questions at the package/application web site." But yet we have here a whole site with support staff for Mathematica? More packages make Mathematica more useful. $\endgroup$
    – JimB
    Mar 11, 2017 at 19:31
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    $\begingroup$ @wolfies: Seeing as "... Combinatorica,or the Groebner basis packages, or the dozens of Wolfram add-on packages..." are supplied by Wolfram at no extra cost, and are not non-free third-party software as is the case here, I think it quite relevant. Else we get the shilling of such packages by the authors with nary a mention that it's a non-free package, seen too often here IMO. This is not an advertising site. $\endgroup$
    – ciao
    Mar 12, 2017 at 0:37

1 Answer 1

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The mathStatica package has an option called VerboseMode which, if activated, states:

 VerboseMode[On]

VerboseMode is now On: integrals sent off to Mathematica will be shown.

Generally, this works as stated. As an example, if you have a random variable $X$ with pdf $f(x)$:

and seek say the $r^{\text{th}}$ order statistic, with VeboseMode on, then Mathematica returns:

.. showing each integral performed by Mathematica, the assumptions used, and the result of each integral.

In the case of the TransformProduct function that the OP asks about, this does not currently work as advertised. I am not sure if this is an oversight, or if because there can be so many integrals involved, and that the way they are combined is not obvious to the end-user, that it might not be ultimately helpful. To illustrate, let us suppose we have 2 random variables, $X$ with pdf $f(x)$:

and $Y$ with pdf $g(y)$:

and we seek the pdf of the product $X Y$:

There are so many integrals involved, which are then added and combined in various ways, that providing the integral inputs and outputs might not be valuable.

At the same time, if VerboseMode states that it shows the integrals performed by Mathematica, then I think the function should do what it says ... and this is something that should, I think, be rectified in a future release.

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