Product ID: 99538

Supplementary Print

Undergraduate

This module presents new and simplified proofs of several theorems, including the arc sine law for sojourn times. The theorems are proved by simple geometry transformations of the paths. The graphical presentation has visual appeal and makes the results accessible to probability students at any level. This module will enable students to understand some of the counterintuitive results of probability theory in applications common to everyday life.** Table of Contents:1. INTRODUCTION2. A VOTING PROBLEM3. PATHS4. COUNTING PATHS USING THE REFLECTION PRINCIPLE5. RANDOM WALKS6. END-POINT PROBABILITIES7. THE PROBABILITY OF STAYING AT LEAST EVEN** 7.1 Proof of Theorem 4

The Transformation

The Transformation T1

The Transformation T2

The Transformation

10. TIME ABOVE ZERO - THE SECOND ARC SINE LAW

The Transformation

12. FURTHER READING

13. SOLUTIONS TO EXERCISES

©1987 by COMAP, Inc.

UMAP Module

34 pages

- Probability & Statistics ,
- Discrete & Finite Mathematics

- Various

Discrete Probability, Combinations

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