Thus a statistic serves to quantify some interesting aspect of the distribution of a variable in a sample. Summary statistics are particularly useful for comparing and contrasting the distribution of a variable …

This book is an introductory text on probability and statistics, targeting students who have studied one year of calculus at the university level and are seeking an introduction to probability and statistics …

This chapter introduces the idea of a probability experi- ment, explains the concept of the probability of an event, and presents the axioms of probability.

The discipline of statistics teaches us how to make intelligent judgments and informed decisions in the presence of uncertainty and variation. Without uncertainty or variation, there would be little need for …

The book is available as a single pdf file or by individual chapters. This is a version of the book as of August 2024 as we have corrected a number of errors and typos.

Probability theory and statistics provide fundamental tools to measure chance, set expectations, estimate parameters, forecast future events, design exper-iments, collect, analyze, and incorporate …

Probability theory is important to empirical sci-entists because it gives them a rational framework to make inferences and test hypotheses based on uncertain empirical data. Probability theory is also …

3.1 Probability and Statistics The basic problem of probability is: Given the distribution of the data, what are the properties (e.g. expectation, variance, etc. ) of the outcomes?

These notes summarize some basic probability and statistics material. The primary sources are A Modern Introduction to Probability and Statistics by Dekking, Kraaikamp, Lopuhaa and Meester, …

The theory and practice of probability and statistics were developed the last century and are still actively being refined and extended. In this we will introduce the basic notions and ideas, and in this first …