Related Experiment Video
Updated: Dec 15, 2025
08:12
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
2.8K
St. Petersburg Paradox and Failure Probability
Jake Fontana1, Peter Palffy-Muhoray2
1U.S. Naval Research Laboratory, 4555 Overlook Avenue Southwest, Washington, DC 20375, USA.
Physical Review Letters
|July 9, 2020
Summary
Researchers experimentally realized the St. Petersburg paradox using tensile fracture. Fracture force was found to depend logarithmically on fiber length, offering insights into failure and reliability in various systems.
Area of Science:
- Physics
- Materials Science
- Probability Theory
Background:
- The St. Petersburg paradox illustrates systems highly sensitive to infrequent, high-impact events.
- Understanding such sensitivity is crucial for predicting system failure and reliability.
Purpose of the Study:
- To provide a physical manifestation of the St. Petersburg paradox.
- To experimentally validate the paradoxical behavior in a material science context.
Main Methods:
- Investigated tensile fracture in fibers.
- Collected six decades of spatial and temporal fracture force data.
- Utilized two distinct material types for robust verification.
Main Results:
- Confirmed a logarithmic relationship between fracture force and fiber length.
- Demonstrated that fracture force is sensitive to rare events, consistent with the St. Petersburg paradox.
Conclusions:
- Tensile fracture serves as a physical model for the St. Petersburg paradox.
- The findings have implications for fields concerned with material failure and reliability analysis.
Related Concept Videos
01:15Binomial Probability Distribution
14.9K
A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
14.9K
01:14Probability in Statistics
21.1K
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
21.1K
00:59Propagation of Uncertainty from Random Error
1.5K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
1.5K
01:09Poisson Probability Distribution
11.4K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
The...
11.4K
01:10Propagation of Uncertainty from Systematic Error
1.2K
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
1.2K
01:14Errors In Hypothesis Tests
5.7K
When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.
5.7K