Strange Show Behavior

Question

When attempting to overlay a Discrete Plot on a Histogram, no matter the order I pass each argument in Show, the Histogram stacks over the Discrete Plot. Is it possible to lay the DiscretePlot over the histogram instead?

Sjoerd Smit · Accepted Answer

If you want to show a histogram and compare it against a PDF, you need to specify the "Probability" (for discrete distributions) or "PDF" (for continuous ones) property to fit the two on top of each other. Otherwise the axes are going to disagree and one plot will swamp out the other:
data = RandomVariate[GeometricDistribution[1/2], 100];
Show[
 Histogram[data, Automatic, "Probability"],
 DiscretePlot[PDF[GeometricDistribution[1/2], x], {x, 0, Max[data]}],
 PlotRange -> All
]

For continuous data:
data = RandomVariate[ExponentialDistribution[1/2], 100];
Show[
 Histogram[data, Automatic, "PDF"],
 Plot[PDF[ExponentialDistribution[1/2], x], {x, 0, Max[data]}],
 PlotRange -> All
]

Daniel Huber · Answer

In Show, Plot options that are given later will override those given earlier. So, make sure your axes fit or do not draw them. There is another possibility. Overlay will simply draw one picture over another.
Here is an example:
d1 = RandomReal[{0, 1}, 100];
g1 = Histogram[d1]
g2 = Plot[30 Sin[2 Pi x], {x, 0, 1}]
Show[{g1, g2}]
Overlay[{g1, g2}]

Strange Show Behavior

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