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It plays 200000 games of craps, finds the number of wins and the number of throws necessary to end each game. The number of wins should be (very close to) a normal with mean 200000p and variance 200000p(1 − p), with p = 244 / 495. Throws necessary to complete the game can vary from 1 to infinity, but counts for all > 21 are lumped with 21.
In mathematics, a Pisot–Vijayaraghavan number, also called simply a Pisot number or a PV number, is a real algebraic integer greater than 1, all of whose Galois conjugates are less than 1 in absolute value. These numbers were discovered by Axel Thue in 1912 and rediscovered by G. H. Hardy in 1919 within the context of Diophantine approximation.
Littlewood conjecture: for any two real numbers ,, ‖ ‖ ‖ ‖ =, where ‖ ‖ is the distance from to the nearest integer. Mahler's 3/2 problem that no real number x {\displaystyle x} has the property that the fractional parts of x ( 3 / 2 ) n {\displaystyle x(3/2)^{n}} are less than 1 / 2 {\displaystyle 1/2} for all positive integers n ...
Every real number can be represented as an integer part followed by a radix point (the generalization of a decimal point to non-decimal systems) followed by a finite or infinite number of digits. If the base is an integer, a terminating sequence obviously represents a rational number. A rational number has a terminating sequence if all the ...
The number of derangements of a set of size n is known as the subfactorial of n or the n th derangement number or n th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include !n, D n, d n, or n¡ . [a] [1] [2] For n > 0 , the subfactorial !n equals the nearest integer to n!/e, where n!
A number normal in base b is rich in base b, but not necessarily conversely. The real number x is rich in base b if and only if the set {x b n mod 1 : n ∈ N} is dense in the unit interval. [11] [12] We defined a number to be simply normal in base b if each individual digit appears with frequency 1 ⁄ b.
Signed zero is zero with an associated sign.In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are equivalent. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero), regarded as equal by the numerical comparison operations but with possible different behaviors in ...
Z tables use at least three different conventions: . Cumulative from mean gives a probability that a statistic is between 0 (mean) and Z.Example: Prob(0 ≤ Z ≤ 0.69) = 0.2549.