### Nguyen, HT, Kreinovich, V and Longpré, L (2004)

#### Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Innite Intervals

Reliable Computing 10(2), 83-106.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1023/B:REOM.0000015848.19449.12

**Abstract:** In many engineering problems, we want a physical characteristic y to lie within given range Y; e.g., for all possible values of the load x from 0 to x_{0}, the resulting stress y of a mechanical structure should not exceed a given value y_{0}. If no such design is possible, then, from the purely mathematical viewpoint, all possible designs are equally bad. Intuitively, however, a design for which y≤y_{0} for all values x∈[0,0.99x_{0}] is more probable to work well than a design for which y≤y_{0} only for the values x∈[0,0.5x_{0}]. In this paper, we describe an interval computations-related formalization for this subjective notion of probability. We show that this description is in good accordance with the empirical distribution of numerical data and with the problems related to estimating the lifetime of the Universe.

**Bibtex:**

```
@article{,
title={Dirty pages of logarithm tables, lifetime of the universe, and (subjective) probabilities on finite and infinite intervals},
author={Nguyen, Hung T and Kreinovich, Vladik and Longpre, Luc},
year={2004},
journal={Reliable Computing},
volume={10},
number={2},
pages={83--106},
doi={10.1023/B:REOM.0000015848.19449.12},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Probability Theory, Statistics