Book Image

Java Data Analysis

By : John R. Hubbard
Book Image

Java Data Analysis

By: John R. Hubbard

Overview of this book

Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the aim of discovering useful information. Java is one of the most popular languages to perform your data analysis tasks. This book will help you learn the tools and techniques in Java to conduct data analysis without any hassle. After getting a quick overview of what data science is and the steps involved in the process, you’ll learn the statistical data analysis techniques and implement them using the popular Java APIs and libraries. Through practical examples, you will also learn the machine learning concepts such as classification and regression. In the process, you’ll familiarize yourself with tools such as Rapidminer and WEKA and see how these Java-based tools can be used effectively for analysis. You will also learn how to analyze text and other types of multimedia. Learn to work with relational, NoSQL, and time-series data. This book will also show you how you can utilize different Java-based libraries to create insightful and easy to understand plots and graphs. By the end of this book, you will have a solid understanding of the various data analysis techniques, and how to implement them using Java.
Table of Contents (20 chapters)
Java Data Analysis
Credits
About the Author
About the Reviewers
www.PacktPub.com
Customer Feedback
Preface
Index

Probability distributions


The probability distribution function (PDF) that is induced by a random variable X is the function fX, defined by:

Here, the expression X = x means the event of all outcomes e for which X(e) = x.

Returning to our coin example, let's compute the probability distribution fX. It is defined on the range of X, which is the set {0, 1, 2, 3, 4}. For example:

In fact, the probability distribution fX for the first version of the coin example is precisely the same as the p(s) function in the second version, tabulated in Table 4-1.

The properties of a probability distribution follow directly from those governing probabilities. They are:

  • 0 f(x) 1, for every x X(S)

  • f(x) = 1

Here is another classic example. The experiment is to toss two balanced dice, one red and one green, and observe the two numbers represented by the dots showing on top. The sample space S has 36 elements:

If the dice are balanced, then each one of these 36 possible outcomes has the same probability...