#### Overview of this book

If you’re a Python developer who wants to discover how to take the power of functional programming (FP) and bring it into your own programs, then this book is essential for you, even if you know next to nothing about the paradigm. Starting with a general overview of functional concepts, you’ll explore common functional features such as first-class and higher-order functions, pure functions, and more. You’ll see how these are accomplished in Python 3.6 to give you the core foundations you’ll build upon. After that, you’ll discover common functional optimizations for Python to help your apps reach even higher speeds. You’ll learn FP concepts such as lazy evaluation using Python’s generator functions and expressions. Moving forward, you’ll learn to design and implement decorators to create composite functions. You'll also explore data preparation techniques and data exploration in depth, and see how the Python standard library fits the functional programming model. Finally, to top off your journey into the world of functional Python, you’ll at look at the PyMonad project and some larger examples to put everything into perspective.
Title Page
Packt Upsell
Contributors
Preface
Free Chapter
Understanding Functional Programming
Introducing Essential Functional Concepts
Functions, Iterators, and Generators
Working with Collections
Recursions and Reductions
The Itertools Module
More Itertools Techniques
The Functools Module
Decorator Design Techniques
Conditional Expressions and the Operator Module
A Functional Approach to Web Services
Optimizations and Improvements
Other Books You May Enjoy
Index

## Computing expected values and displaying a contingency table

The expected defect production is a combined probability. We'll compute the shift defect probability multiplied by the probability based on defect type. This will allow us to compute all 12 probabilities from all combinations of shift and defect type. We can weight these with the observed numbers and compute the detailed expectation for defects.

The following code calculates expected values:

```expected = {
(s, t): P_shift[s]*P_type[t]*total
for t in P_type
for s in P_shift
} ```

We'll create a dictionary that parallels the initial `defects``Counter` object. This dictionary will have a sequence of two-tuples with keys and values. The keys will be two-tuples of shift and defect type. Our dictionary is built from a generator expression that explicitly enumerates all combinations of keys from the `P_shift` and `P_type` dictionaries.

The value of the `expected` dictionary looks like this:

```{('2', 'B'): Fraction(2208, 103),
('2', 'D'): Fraction...```