Chapter 3 Probability, Conditional Probability, and Bayes’ Rule
Ultimately, in my extreme view, all reasoning reduces to probability calculations.
– Dennis Victor Lindley
3.1 Introduction
If statistics can be defined as the science that studies uncertainty, then probability is the branch of mathematics that quantifies it. One's intuition of chance and probability develops at a very early age(Piaget and Inhelder, 1976). However, the formal, precise definition of probability is elusive. There are several competing definitions for the probability of an event,butthe most practical one usesits relative frequency in a potentially infinite series of experiments.
Probability is a part of all introductory statistics programs for a good reason: it is the theoretical foundation of statistics. The basic statistical concepts of random sample, sampling distributions, statistic, etc., require familiarity with probability to be understood, explained, and applied.
Probability is critical for the development of statistical concepts. Despite this fact, it will not be a focal point of this text. There is a dangerous temptation to dwell on urns,black and white ...
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