#!/usr/bin/env python
# coding: utf-8

# In[1]:


from IPython.display import Image 
Image('../../../python_for_probability_statistics_and_machine_learning.jpg')


# [Python for Probability, Statistics, and Machine Learning](https://www.springer.com/fr/book/9783319307152)

# To get started thinking about statistics, consider the three famous problems
# 
# * Suppose you have a bag filled with colored marbles. You close your eyes and
#   reach into it and pull out a handful of marbles, what can you say about what is
#   in the bag?
# 
# * You arrive in a strange town and you need a taxicab. You look out the window,
#   and in the dark, you can just barely make out the number on the roof of one of
#   the cabs. In this town, you know they label the cabs sequentially. How many
#   cabs does the town have?
# 
# * You have already taken the entrance exam twice and you want to know if it's
#   worth it to take it a third time in the hopes that your score will improve.
#   Because only the last score is reported, you are worried that you may do worse
#   the third time. How do you decide whether or not to take the test again?
# 
# Statistics provides a structured way to approach each of these problems.  This
# is important because it is easy to be fooled by your biases and intuitions.
# Unfortunately, the field does not provide a *single* way to do this, which
# explains the many library shelves that groan under the weight of statistics
# texts. This means that although many statistical quantities are easy to
# *compute*, these are not so easy to justify, explain, or even understand.
# Fundamentally, when we start with just the data, we lack the underlying
# probability density that we discussed in the last chapter. This removes key
# structures that we have to compensate for in however we choose to process the
# data.  In the following, we consider some of the most powerful statistical
# tools in the Python arsenal and suggest ways to think through them