منابع مشابه
Colliding Dice Probabilities
LetK, L be congruent regular polyhedra in R. Let g denote a rigid motion of R, that is, g(x) = Φx+τ where Φ is a 3×3 rotation matrix and τ is a translation 3-vector. The polyhedraK, g(L) are said to touch ifK∩g(L) 6= ∅ but int(K)∩int(g(L)) = ∅. Alternatively, we may think of ΦL moving toward K in the direction τ , stopping precisely when the two polyhedra collide. Let us sample the space SO3 of...
متن کاملOn Estimating the Face Probabilities of Shaved Dice With Partial Data
As noted by Persi Diaconis, the apparently simple problem of estimating the face probabilities of a shaved die defies exact mathematical analysis. However, this problem can be used to provide amusing and instructive examples of sufficiency, efficiency, information, ancillarity, and the value of statistical design.
متن کاملTied dice
A generalized die is a list (x1; :::; xn) of integers. For integers n 1, a b and s let D(n; a; b; s) be the set of all dice with a x1 ::: xn b and P xi = s. Two dice X and Y are tied if the number of pairs (i; j) with xi < yj equals the number of pairs (i; j) with xi > yj . We prove the following: with one exception (unique up to isomorphism), if X 6= Y 2 D(n; a; b; s) are tied dice neither of ...
متن کاملDice graphs
For integers n 1, a b and s let D(n; a; b; s) be the set of all lists of integers (x1; :::; xn) with a x1 ::: xn b and P xi = s. There is a graph G(n; a; b; s) with vertex-set D(n; a; b; s) in which two vertices are adjacent if one is stronger than the other in a natural dice game. In The prevalence of paradoxical dice [Bull. Inst. Combin. Appl. 45 (2005), 70-76] the dice which are isolated v...
متن کاملConcerning Dice and Divinity
Einstein initially objected to the probabilistic aspect of quantum mechanics— the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein saw as the abandonment of physical realism. We argue here that Einstein's initial intuition was perfectly sound, and that it is precisely the fact that quantum ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Lietuvos matematikos rinkinys
سال: 2009
ISSN: 2335-898X,0132-2818
DOI: 10.15388/lmr.2009.22