On the representation of a certain fundamental law of probability
| Autor: | H. L. Rietz |
|---|---|
| Rok vydání: | 1925 |
| Předmět: |
Pure mathematics
Law of total expectation Uniform distribution (continuous) Laplace transform Distribution (number theory) Applied Mathematics General Mathematics Infinitesimal Law of total probability Range (statistics) Astrophysics::Earth and Planetary Astrophysics Law of the unconscious statistician Mathematics |
| Zdroj: | Transactions of the American Mathematical Society. 27:197-212 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/s0002-9947-1925-1501307-5 |
| Popis: | gives, to within infinitesimals of higher order, the probability that the sum of n elements each taken at random from a given range 0 to a (a 0) of uniform distribution, will fall into the interval x to x + dx. Laplace applied the above formula to the historic problem+ of finding the probability that the inclinations of the orbits of the ten planets besides the earth known at the beginning of the year 1801 do not constitute a random distribution. When Laplace proceeded to apply his theory to the orbits of all comets? known at the end of the year 1811, the number n in formula (1) was so large as to render the formula impracticable for numerical computation. Laplacell used the form |
| Databáze: | OpenAIRE |
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