How to produce ListPlot that samples a given distribution?

Question

I wanted to get a binned plot that a uniform background distribution with a spike at some bin. My first instinct was to use RandomVariate, and then ListPlot. What i get is this

This makes sense as the RandomVariate function is assigning a value to Y based on the distribution. But I was wondering how I would produce a plot that has a spike at some particular bin (some specified x). I would want to produce something that looks more like this, for example.

I know I could just manually enter the data, but is there a way to have a binned plot where there is a uniform background distribution and a gaussian peak at some specific x?

Answer 1

You are on the right track. Notice that in your mixture, the uniform distribution spans [0,2], but the Normal distribution has a mean of 3. Here is another mixture. Just adjust the distribution parameters as needed:

dist = MixtureDistribution[{1, 1},
   {
    UniformDistribution[{0, 100}],
    NormalDistribution[50, 2]
    }
   ];

Histogram[RandomVariate[dist, 1000], {1}]

Edit: If you want data, you can use some variant of HistogramList:

{binBoundaries, counts} = 
  HistogramList[RandomVariate[dist, 1000], {1}];

ListPlot[Transpose[{Most[binBoundaries], counts}], PlotRange -> All, 
 Filling -> Axis]