Book contents
- Front matter
- CONTENTS
- Preface to the First Edition
- Preface to the Second Edition
- Preface to the Third Edition
- Abbreviations and Notations
- FIRST PART PRINCIPLES
- Chapter I Introductory remarks
- Chapter II Axioms and preliminary theorems
- SECOND PART DISTRIBUTIONS IN R1
- THIRD PART DISTRIBUTIONS IN RK
- Bibliography
- Some Recent Works on Mathematical Probability
Chapter I - Introductory remarks
Published online by Cambridge University Press: 22 September 2009
- Front matter
- CONTENTS
- Preface to the First Edition
- Preface to the Second Edition
- Preface to the Third Edition
- Abbreviations and Notations
- FIRST PART PRINCIPLES
- Chapter I Introductory remarks
- Chapter II Axioms and preliminary theorems
- SECOND PART DISTRIBUTIONS IN R1
- THIRD PART DISTRIBUTIONS IN RK
- Bibliography
- Some Recent Works on Mathematical Probability
Summary
In the most varied fields of practical and scientific experience, cases occur where certain observations or trials may be repeated a large number of times under similar circumstances. Our attention is then directed to a certain quantity, which may assume different numerical values at successive observations. In many cases each observation yields not only one, but a certain number of quantities, say k, so that generally we may say that the result of each observation is a definite point X in a space of k dimensions (k ≥ 1), while the result of the whole series of observations is a sequence of points: X1, X2, ….
Thus if we make a series of throws with a given number of dice, we may observe the sum of the points obtained at each throw. We are then concerned with a variable quantity, which may assume every integral value between m and 6m (both limits inclusive), where m is the number of dice. On the other hand, in a series of measurements of the state of some physical system, or of the size of certain organs in a number of individuals belonging to the same biological species, each observation furnishes a certain number of numerical values, i.e. a definite point X in a space R of a fixed number of dimensions.
In certain cases, the observed characteristic is only indirectly expressed as a number.
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- Information
- Random Variables and Probability Distributions , pp. 1 - 8Publisher: Cambridge University PressPrint publication year: 1970