bugs - Random variables with transformed discrete distributions cannot be applied to Probability[] function?

I have two discrete uniform distributions over same support:

Dx = DiscreteUniformDistribution[{-8, 8}];  
Dy = DiscreteUniformDistribution[{-8, 8}];

I use random variables X $\sim$ Dx, Y $\sim$ Dy to model condition in some if-else clause in C code. For example,

if (3 * x + 1 > y) {
   ... 
}

So, I model this condition by random event 3*X + 1 > Y. Then probability I look for is:

Probability[
  x > y, 
  {Distributed[x, TransformedDistribution[3 * x + 1, Distributed[x, Dx]]],
   Distributed[y, Dy]}
]

Unfortunately, Mathematica produces nothing. As for me, this is very strange behavior because Mathematica also cannot compute mean for the product distribution of {X, Y}. Maybe, this problem is caused by different support of X and Y.

How can I compute this probability?

Answer

The following computes the probability you asked for, but I'm at a loss to understand why your notation won't work. It seems correct to me.

Probability[
 3 x + 1 > y, {Distributed[x, Dx], Distributed[y, Dy]}]

(*
==> 147/289
*)

The Probability / Distribution functions are quite young and hence not fully bulletproofed and I have encountered a number of bugs myself. I suppose/hope that in the next release they will be solved. I suggest you contact Wolfram support (support@wolfram.com). But perhaps someone else here may find out what's wrong.

A few of mine:

No random variates from PDFs that stem from multivariate distributions:

dist = ProbabilityDistribution[
   PDF[BinormalDistribution[{0, 0}, {1, 1}, 0]][{x, 
     y}], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}];
RandomVariate[dist]

This works for 3, but not for 5 (and higher):

Expectation[x,x\[Distributed] OrderDistribution[{GeometricDistribution[0.1], 3}, 3]]
Expectation[x,x\[Distributed] OrderDistribution[{GeometricDistribution[0.1], 5}, 5]]

The following crashes the kernel after a minute or so (so, DO NOT EXECUTE):

PDF[TransformedDistribution[Sin[u], u \[Distributed] NormalDistribution[0, 1]], 0]

Comments

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I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....

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