Probability Mass Functions

Chapter 3 Probability Mass Functions

In the previous chapter we represented distributions using a FreqTab object, which contains a set of values and their frequencies — that is, the number of times each value appears. In this chapter we’ll introduce another way to describe a distribution, a probability mass function (PMF).

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To represent a PMF, we’ll use an object called a Pmf, which contains a set of values and their probabilities. We’ll use Pmf objects to compute the mean and variance of a distribution, and the skewness, which indicates whether it is skewed to the left or right. Finally, we will explore how a phenomenon called the "inspection paradox" can cause a sample to give a biased view of a distribution.

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Listing 3.0.1. Python Code

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from os.path import basename, exists


def download(url):
    filename = basename(url)
    if not exists(filename):
        from urllib.request import urlretrieve

        local, _ = urlretrieve(url, filename)
        print("Downloaded " + local)


download("https://github.com/AllenDowney/ThinkStats/raw/v3/nb/thinkstats.py")

Listing 3.0.2. Python Code

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try:
    import empiricaldist
except ImportError:
    %pip install empiricaldist

Listing 3.0.3. Python Code

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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

from thinkstats import decorate

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