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