Topic
Central binomial coefficient
About: Central binomial coefficient is a research topic. Over the lifetime, 696 publications have been published within this topic receiving 21198 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 1950
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Abstract: Office hours: MWF, immediately after class or early afternoon (time TBA). We will cover the mathematical foundations of probability theory. The basic terminology and concepts of probability theory include: random experiments, sample or outcome spaces (discrete and continuous case), events and their algebra, probability measures, conditional probability A First Course in Probability (8th ed.) by S. Ross. This is a lively text that covers the basic ideas of probability theory including those needed in statistics. Theoretical concepts are introduced via interesting concrete examples. In 394 I will begin my lectures with the basics of probability theory in Chapter 2. However, your first assignment is to review Chapter 1, which treats elementary counting methods. They are used in applications in Chapter 2. I expect to cover Chapters 2-5 plus portions of 6 and 7. You are encouraged to read ahead. In lectures I will not be able to cover every topic and example in Ross, and conversely, I may cover some topics/examples in lectures that are not treated in Ross. You will be responsible for all material in my lectures, assigned reading, and homework, including supplementary handouts if any.
10,221 citations
1,553 citations
522 citations
TL;DR: Fisher's "exact" (one-sided) test may be used to test the null hypothesis p1 = p2, against the alternative hypothesis that pl > p2.
Abstract: If x and y are each binomially distributed with index n and parameters pl and p2 respectively, then the comparison of these two binomial distributions is usually displayed as a 2 X 2 table and Fisher's "exact" (one-sided) test may be used to test the null hypothesisp1 = p2, against the alternative hypothesis that pl > p2. The exact test is based on arguing conditionally on the observed number of"successes", i.e., x + y, see Yates (1934) and Fisher (1935). The distribution of x with x + y = m fixed depends on pl and P2 only through the odds ratio 0 = (p1q2)/(q,p2), where qi 1-Pi rhe conditional distribution is Pr (x 1 0) C (n,x) C (n,y) AX/zzC(n,i)C(n,m-i)0i, where i takes the values L = max(O, m-n) to U = min(n, m). Let xc be the critical value of x for the exact test of P1 > P2 (i.e., 0 > 1 ) against the null hypothesis 0 = 1 with type I error oe, so that
435 citations
Book•
1 Nov 2008
TL;DR: In this paper, the central binomial coefficient and binomial coefficients are revisited and the central Binomial Coefficient is revisited with a family of binary words and a Catalan triangle.
Abstract: 1. Bionomial Coefficients 2. The Central Binomial Coefficient 3. The Central Binomial Coefficient Revisited 4. Binomial Coeffiecients Revisited 5. Catalan Numbers 6. The Ubiquity of Catalan Numbers I 7. The Ubiquity of Catalan Numbers II 8. Trees and Catalan Numbers 9. Lattice Paths and Catalan Numbers 10. Partitions and Catalan Numbers 11. Algebra, Sports, and Catalan Numbers 12. Catalan Numbers and Pascal's Triangle 13. Divisibilty Properties 14. A Catalan Triangle 15. A Family of Binary Words 16. Tribinomial Coefficients 17. Generalized Catalan Numbers
384 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 6 |
| 2024 | 16 |
| 2023 | 19 |
| 2022 | 66 |
| 2021 | 14 |
| 2020 | 7 |