Corpus ID: 211010603

The Petersburg paradox and failure probability.

@article{Fontana2020ThePP,
  title={The Petersburg paradox and failure probability.},
  author={Jake Fontana and Peter Palffy-Muhoray},
  journal={arXiv: Applied Physics},
  year={2020}
}
The Petersburg paradox provides a simple paradigm for systems that show sensitivity to rare events. Here, we demonstrate a physical realization of this paradox using tensile fracture, experimentally verifying for six decades of spatial and temporal data and two different materials that the fracture force depends logarithmically on the length of the fiber. The Petersburg model may be useful in a variety fields where failure and reliability are critical. 
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References

SHOWING 1-9 OF 9 REFERENCES
An Introduction To Probability Theory And Its Applications
TLDR
A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics. Expand
Proceedings of the National Academy of Sciences, USA
TLDR
The song below is a talking blues in the style of Woody Guthrie, written by Joel Herskowitz, a pediatric neurologist working in Boston, and sung by Joel and his brother Ira. Expand
Advances in Physics 55
  • 349
  • 2006
Phys
  • Rev. E 62, 1622
  • 2000
Physical Review Letters 63
  • 1989
Mechanical metallurgy
  • Vol. 3
  • 1986
Phys
  • 35
  • 1984
Journal of Applied Mechanics-Transactions of the Asme 18
  • 293
  • 1951
A history of the mathematical theory of probability (Chelsea
  • New York,
  • 1949