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I'm assuming that I didn't define my color function correctly, because if, for example, I use the built-in color functions like "DarkRainbow," both plots behave as expected. … So what needs to be changed in my color function definition to get the desired output? Also, if I turn off color function scaling, how do I control which values get mapped to each color? …

The only way that I can think of to effectively visualize this in Mathematica would be to use an ArrayPlot with the $x$ and $n$ being the axes and one of $P(X=x)$ or $p$ being mapped to a color function …

Suppose I want to define a color function to use more than one graph. I'd prefer not to type it out every time. … For example, if I try to do something like this: Unprotect[ColorFunction]; ColorFunction["myCF"] = Function[{y}, ColorData["myRainbow"][y]]; Protect[ColorFunction]; and then try to call that color function …

Observe the following Mathematica code. Forgive me that it's so long: test[y_] := ArrayPlot[Table[nd[y, 1, K, n], {K, 1, 15}, {n, 1, 15}], ColorFunction -> "DarkRainbow", ColorFunctionScaling - …

26% should be mapping to a color somewhere around Purple/Blue, but it's getting mapped all the way up to the color white! … Can somebody please explain what is going on and what I need to do to get the desired color output? …

Either way, that hideous red color is consistent regardless of the color scheme that I use. For example, with DarkRainbow: It's the exact same shade of red. … Is it possible to change this dark red color? …

Does Mathematica not recognize what the color black is? Hello? I just don't understand why it's doing this. … It works for literally any color other than black. Obviously there are easy workaround to this, like choosing another color that's really close to black, but seriously, what's going on here? …