Cumulative Distribution Function from an image histogram

A histogram of a continuous random variable is sometimes called a Probability Distribution Function (or PDF). The area under a PDF (a definite integral) is called a Cumulative Distribution Function (or CDF). The CDF quantifies the probability of observing certain pixel intensities.

Your task here is to plot the PDF and CDF of pixel intensities from a grayscale image. You will use the grayscale image of Hawkes Bay, New Zealand (originally by Phillip Capper, modified by User:Konstable, via Wikimedia Commons, CC BY 2.0). This time, the 2D array image will be pre-loaded and pre-flattened into the 1D array pixels for you.

The histogram option cumulative=True permits viewing the CDF instead of the PDF.
Notice that plt.grid('off') switches off distracting grid lines.
The command plt.twinx() allows two plots to be overlayed sharing the x-axis but with different scales on the y-axis.

First, use plt.hist() to plot the histogram of the 1-D array pixels in the bottom subplot.
Use the histogram options bins=64, range=(0,256), and normed=False.
Use the plotting options alpha=0.4 and color='red' to make the overlayed plots easier to see.
Second, use plt.twinx() to overlay plots with different vertical scales on a common horizontal axis.
Third, call plt.hist() again to overlay the CDF in the bottom subplot.
Use the histogram options bins=64, range=(0,256), and normed=True.
This time, also use cumulative=True to compute and display the CDF.
Also, use alpha=0.4 and color='blue' to make the overlayed plots easier to see.

Take Hint (-30 XP)

Exercise

Cumulative Distribution Function from an image histogram

Instructions