Please, do read the Preface first!

Note. Capitalized ‘Probability’ and ‘Statistics’ (when they do not start a sentence) here refer to the subjects. Thus, Probability is the study of probabilities, and Statistics that of statistics. (Later, we shall also use ‘Statistics’ as opposed to ‘statistics’ in a different, technical, way.) ‘Maths’ is English for ‘Math’, ‘Mathematics’ made friendly.

Conditioning: an intuitive first look

One of the main aims of this book is to teach you to ‘condition’: to use conditional probabilities and conditional expectations effectively. Conditioning is an extremely powerful and versatile technique.

In this section and (more especially) the next, I want you to give your intuition free rein, using common sense and not worrying over much about rigour. All of the ideas in these sections will appear later in a more formal setting. Indeed, because fudging issues is not an aid to clear understanding, we shall study things with a level of precision very rare for books at this level; but that is for later. For now, we use common sense, and though we would later regard some of the things in these first two sections as ‘too vague’, ‘non-rigorous’, etc, I think it is right to begin the book as I do. Intuition is much more important than rigour, though we do need to know how to back up intuition with rigour.