Generalization of Arithmetico-Geometric Series and the Expectation Value of a $k$-Run of a Bernoulli Trial
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916500549402624 |
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| author | Khare, Priyansh |
| author_facet | Khare, Priyansh |
| contents | The article uses an arithmetic-geometric Fibonacci series to find the expected value of trials needed to observe k consecutive successes for the first time in a Bernoulli experiment using a recurrence relation. It is important to note that this is not a new result, but to the best of the authors' knowledge at the time of uploading, this is a novel derivation of a well-established result. The other derivations of this result are cited in the references section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00002 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalization of Arithmetico-Geometric Series and the Expectation Value of a $k$-Run of a Bernoulli Trial Khare, Priyansh History and Overview Probability The article uses an arithmetic-geometric Fibonacci series to find the expected value of trials needed to observe k consecutive successes for the first time in a Bernoulli experiment using a recurrence relation. It is important to note that this is not a new result, but to the best of the authors' knowledge at the time of uploading, this is a novel derivation of a well-established result. The other derivations of this result are cited in the references section. |
| title | Generalization of Arithmetico-Geometric Series and the Expectation Value of a $k$-Run of a Bernoulli Trial |
| topic | History and Overview Probability |
| url | https://arxiv.org/abs/2412.00002 |