|
3 |
Functions of Random Variables and Geometric Probability |
|
3.1 |
Functions of Random Variables: Derived Distributions |
|
3.2 |
Perturbation Methods |
| |
3.2.1 |
Perturbations to a Random Variable |
| |
3.2.2 |
Perturbations to a PDF |
| |
3.2.3 |
Perturbations to a Sample Space |
|
3.3 |
Geometric Probability |
| |
3.3.1 |
Buffon's Needle Experiment |
| |
3.3.2 |
Bertrand's Paradox |
| |
3.3.3 |
Cauchy Distribution |
|
3.4 |
Assumption of Uniformity |
| |
3.4.1 |
A Geometrical Probability Interpretation of PDF's |
|
3.5 |
Crofton's Method for Computing Mean Values |
| |
3.5.1 |
Response Distance of an Ambulette Revisited |
| |
3.5.2 |
Summary of Method |
|
3.6 |
Coverage |
|
3.7 |
Expected Travel Distances and Times: Some Practical Results |
| |
3.7.1 |
Simple Model |
| |
3.7.2 |
More Realistic Travel-Time Model |
| |
3.7.3 |
Expected Travel Distances: The General Case |
|
3.8 |
Spatial Poisson Processes |
| |
3.8.1 |
Description and Postulates |
| |
3.8.2 |
Time-space Poisson Process |
| |
3.8.3 |
Application to Facility Location and Districting |
|
3.9 |
Alternative Spatial Processes |
| |
3.9.1 |
Spread Process Yielding the Binomial PMF |
| |
3.9.2 |
Clustered Process Yielding the Negative Binomial PMF |
|
3.10 |
Conclusion |
|
*** |
References |
|
*** |
Problems |
