Showing papers in "American Mathematical Monthly in 1951"
TL;DR: In this article, a tabular summary of parametric families of distributions is presented, along with a parametric point estimation method and a nonparametric interval estimation method for point estimation.
Abstract: 1 probability 2 Random variables, distribution functions, and expectation 3 Special parametric families of univariate distributions 4 Joint and conditional distributions, stochastic independence, more expectation 5 Distributions of functions of random variables 6 Sampling and sampling distributions 7 Parametric point estimation 8 Parametric interval estimation 9 Tests of hypotheses 10 Linear models 11 Nonparametric method Appendix A Mathematical Addendum Appendix B tabular summary of parametric families of distributions Appendix C References and related reading Appendix D Tables
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228 citations
TL;DR: In this paper, it was shown that the number 18 cannot be replaced by a smaller number, as is shown by the example in which all of the circles have radius 1 and the centers are at the following points in a polar coordinate system: the origin, the points (1, h. 60’) where h=O, 1,. e., 5, and the points(2 cos 15’, (2K+l). 15”) where K=O.
Abstract: Besicovitch proved the weaker theorem obtained from this one by replacing 18 by 21. In this paper we shall prove Theorem 1 as it stands. The number 18 cannot be replaced by a smaller number, as is shown by the example in which all of the circles have radius 1 and the centers are at the following points in a polar coordinate system: the origin, the points (1, h. 60’) where h=O, 1, . e . , 5, and the points (2 cos 15’, (2K+l). 15”) where K=O, 1, . * , Il. We prove Theorem 1 by establishing its equivalence with Theorem 2 and then proving the latter.
69 citations
TL;DR: A Half-Century of Mathematics as discussed by the authors is a collection of essays about mathematics from the 1950s to the 1990s, with a focus on the half-century of mathematics.
Abstract: (1951). A Half-Century of Mathematics. The American Mathematical Monthly: Vol. 58, No. 8, pp. 523-553.
50 citations
25 citations
TL;DR: The History of Calculus as mentioned in this paper is a history of the history of calculus and its application in the computer science field, with a focus on algebraic geometry, and includes the following topics:
Abstract: (1951). The History of Calculus. The American Mathematical Monthly: Vol. 58, No. 2, pp. 75-86.
23 citations
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TL;DR: The Story of Tangents as discussed by the authors is a collection of tangents from the story of the tangents of Tangent-to-Tangents (Tangent-To-Tangent).
Abstract: (1951). The Story of Tangents. The American Mathematical Monthly: Vol. 58, No. 7, pp. 449-462.
TL;DR: The Foremost Textbook of Modern Times as discussed by the authors is the most widely used textbook of modern times for algebraic geometry and its applications in computer science and computer science, and can be found here.
Abstract: (1951). The Foremost Textbook of Modern Times. The American Mathematical Monthly: Vol. 58, No. 4, pp. 223-226.
TL;DR: In this paper, modern college geometry, Modern College Geometry, Modern college geometry (MCEG), Modern college geometry (MLG), MCEG, modern college geometrical geometry (WCG),
Abstract: Modern college geometry , Modern college geometry , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
TL;DR: In this article, the Institute for Numerical Analysis of the National Bureau of Standards (INA) published a paper "The American Mathematical Monthly: Vol. 58, No. 6, pp. 372-379".
Abstract: (1951). The Institute for Numerical Analysis of the National Bureau of Standards. The American Mathematical Monthly: Vol. 58, No. 6, pp. 372-379.
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TL;DR: In this paper, the behavior of B(x, y) over all real x and y for which the Beta function is defined is discussed, and the discussion is greatly facilitated by graphic aids.
Abstract: The First Eulerian Integral, called the Beta Function, is defined by B(x, y) =folt-1(1 -t)Y-ldt, which converges for x > 0 and y > 0. The well-known equation connecting the Beta and Gamma functions, B(x, y) = r(x)r(y)/r(x+y), is therefore valid only for positive real x and y. However, this relation is commonly used as a definition, to extend B(x, y) so that the function has meaning for values other than positive real x, y. It is the purpose of this paper to discuss the behavior of B(x, y) over all real x and y for which the function is thus defined. The discussion is greatly facilitated by graphic aids. Since B(x, y) is continuous (with isolated exceptions) over the regions of definition, it can be represented by a Cartesian surface, z=B(x, y). In particular, z is continuous for all x>0, y>0, and so is represented by a smooth unbroken surface throughout the first octant (Fig. 1). Since it is obvious from the extended definition that B(x, y)