Include density cumulative function

_episodes/03-plotting.md

@@ -600,7 +600,7 @@ plt.title(f"Normal distribution - mean={mean}, stdev={stdev}, samples={samples},
 > to have a nicely typeset `μ` character in the title.
 > Doing full stylization with LaTeX we could use:
 > ~~~
-> plt.title(f"$X \\sim \\mathcal{N}(\\mu,\\,\\sigma^{2})$ - $\\mu$={mean}, $\\sigma^{2}$={stdev}, samples={samples}, binning={1/bins}")
+> plt.title(f"$X \\sim \\mathcal{{N}}(\\mu,\\,\\sigma^{{2}})$ - $\\mu$={mean}, $\\sigma^{{2}}$={stdev}, samples={samples}, binning={1/bins}")
 > ~~~
 > {: .language-python }
 >
@@ -615,10 +615,42 @@ plt.title(f"Normal distribution - mean={mean}, stdev={stdev}, samples={samples},
 > by prefixing it with `r`, becoming `r"\alpha"`.
 {: .callout }
 
-## Scatter
+> ## A Dense Histogram
+>
+> Exploring the [documentation of `plt.hist()`][matplotlib-hist], find how to add
+> a *probability density* projection of the plot above.
+>
+> When plotting as density, the values in the `Y` axis change.
+> Is this representation easier to understand than the default histogram with counts?
+> What if in addition the histogram is made cumulative?
+>
+> > ## Solution
+> >
+> > The `plt.hist()` function accepts a `density=True` and a `cumulative=True` option.
+> > Although the `Y` axis values change, the bars should have the same visual representation
+> > (unless a new random sample was generated).
+> >
+> > A density plot transforms the `Y` scale such that the area under the histogram
+> > adds to `1`.
+> > A value of `0.40` implies that the area occupied by the central bar represents 40% of the points.
+> > ~~~
+> > plt.hist(normal_dist, bins, density=True)
+> > ~~~
+> > {: .language-python }
+> > ![Histogram as density](../fig/normal-hist-density.png)
+> >
+> > A perhaps more intuitive plot, is represented by the cumulative density, which
+> > as previously described should add to `1`.
+> > ~~~
+> > plt.hist(normal_dist, bins, density=True, cumulative=True)
+> > ~~~
+> > {: .language-python }
+> > ![Histogram as cumulative density](../fig/normal-hist-cumuldensity.png)
+> >
+> {: .solution }
+{: .challenge }
+
 ## Bar
-## Histograms
-## Subplots
 
 - the next exercise assumes an example of subplots arranged in a single row or column