A Natural Introduction to Probability Theory （2003. XI, 191 p. w. figs. 24 cm）

A Natural Introduction to Probability Theory （2003. XI, 191 p. w. figs. 24 cm）

  • ただいまウェブストアではご注文を受け付けておりません。 ⇒古書を探す
  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 220 p.
  • 商品コード 9783764321888

基本説明

Undergraduate textbook.

Full Description


In this introduction to probability theory, we deviate from the route usually taken. We do not take the axioms of probability as our starting point, but re-discover these along the way. First, we discuss discrete probability, with only probability mass functions on countable spaces at our disposal. Within this framework, we can already discuss random walk, weak laws of large numbers and a first central limit theorem. After that, we extensively treat continuous probability, in full rigour, using only first year calculus. Then we discuss infinitely many repetitions, including strong laws of large numbers and branching processes. After that, we introduce weak convergence and prove the central limit theorem. Finally we motivate why a further study would require measure theory, this being the perfect motivation to study measure theory. The theory is illustrated with many original and surprising examples.

Contents

Preface * Experiments * Random Variables and Random Vectors * Random Walk * Limit Theorems * Intermezzo * Continuous Random Variables and Vectors * Infinitely Many Repetitions * The Poisson Process * Limit Theorems * Extending the Probabilities * Interpreting Probabilities * Further Reading * Answers to Selected Exercises * Index.