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The problem of random intervals on a line
| Content Provider | Scilit |
|---|---|
| Author | Domb, C. |
| Copyright Year | 1947 |
| Description | Suppose that events occur at random points on a line from t = −∞ to +∞, the probability of an event occurring between t and t + dt being λdt. If we select any interval of the line, say the interval [0, y], there will be a finite probability that it contains 0, 1, 2,…,r,…events; in fact, it is not difficult to show that these probabilities form a Poisson distribution, the probability that the interval contains r events being (see e.g. (1)). Consider the case when each event consists of an interval of length α (an event being characterized by its first point). What is the probability that the covered portion of the interval [0, y] lies between x and x + dx? |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D2E6712C3B3A90AD42AE0BD573DDD83F/S0305004100023562a.pdf/div-class-title-the-problem-of-random-intervals-on-a-line-div.pdf |
| Ending Page | 341 |
| Page Count | 13 |
| Starting Page | 329 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004100023562 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 3 |
| Volume Number | 43 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1947-07-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
