I have about 200 real numbers spread over the range 0-400.  I use `HistogramDistribution` to bin them and `PDF` to create the resulting step-wise probability distribution. I assumed that `CDF` applied to the `HistogramDistribution` would yield a continuous, piece-wise linear function, but I keep getting these annoying gaps in the plot of the CDF. 

Here's the code I'm using applied to some random data:

    data = Table[400*RandomReal[], {200}];
    pd = PDF[HistogramDistribution[data, 20]];
    Plot[pd[x], {x, 0, 400}]
    Plot[CDF[HistogramDistribution[data, 20], x], {x, 0, 400}]

Any idea what's causing the gaps and how to get rid of them?