# Removing Magic from the Normal Distribution and the Stirling and Wallis Formulas

## Related Articles

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The Legendre duplication formula for the gamma function is derived from the normal distribution. Its connection with the binomial distribution is also discussed. A classical integral formula in terms of gamma functions is obtained as a byproduct of the normal derivation.

- INFORMATION MATRIX FOR GENERALIZED SKEW--NORMAL DISTRIBUTIONS. G�MEZ, H�CTOR W.; SALINAS, HUGO S. // Proyecciones - Journal of Mathematics;2010, Vol. 29 Issue 2, p83
The Fisher information matrix for Generalized skew-normal (GSN) distribution is derived. The expressions for the elements of the matrices require of integrals that are solved numerically using a suitable software.

- DERIVED CATEGORIES OF SMALl TORIC CALABI—YAU 3-FOLDS AND CURVE COUNTING INVARIANTS. Nagao, Kentaro // Quarterly Journal of Mathematics;Dec2012, Vol. 63 Issue 4, p965
We first construct a derived equivalence between a small crepant resolution of an affine toric Calabiâ€“Yau 3-fold and a certain quiver with a superpotential. Under this derived equivalence, we establish a wall-crossing formula for the generating function of the counting invariants of...

- Letters to the Editor. Hitotumatu, Sin // Mathematical Intelligencer;Summer2003, Vol. 25 Issue 3, p4
Presents an alternative proof for the sum of the first n squares and for the sum of the first n factorials of order two. Association of n squares with the triangular number; Representation of the sum of the first n squares using the tetrahedral number.

- Approximation by Normal Distribution in Generalized Allocation Scheme and its Applications. MIRAKHMEDOV, SHERZAD // Australian Journal of Basic & Applied Sciences;2011, Vol. 5 Issue 2, p157
A random vector of frequencies of cells in the generalized allocation scheme of particles into cells is defined through conditional distribution of a random vector with integer, non-negative and independent components given their sum. A wide class of statistics, viz. the sum of functions of the...

- A DIRECT JUSTIFICATION OF THE BINOMIAL PRICING MODEL AS AN APPROXIMATION OF THE BLACK-SCHOLES FORMULA. Xianggui Qu // Pakistan Journal of Statistics;2010, Vol. 26 Issue 1, p187
This paper pedagogically presents a proof of the binomial option pricing model as an approximation of the Black-Scholes formula. The proof only requires basic calculus and a direct approximation of the binomial probability by the normal distribution is used.

- Normal & Binomial Distributions. Wienclaw, Ruth A. // Normal & Binomial Distributions -- Research Starters Business;4/1/2018, p1
The normal distribution is a family of idealized bell-shaped curves derived from a mathematical equation. Normal distributions are unimodal, symmetrical about the mean, and have an area that is always equal to 1. In addition, normal distributions are continuous rather than discrete and are...

- A bernoulli scheme with abstract probabilities. Maximov, V. // Doklady Mathematics;Sep2014, Vol. 90 Issue 2, p603
The article discusses the two approaches of the Bernoulli scheme with abstract probabilities. It outlines the function of the two approaches which were introduced by various mathematicians and describes how they can be applied to the case of adic probabilities. It also recalls the basic...

- Symmetric generalized binomial distributions. Bergeron, H.; Curado, E. M. F.; Gazeau, J. P.; Rodrigues, Ligia M. C. S. // Journal of Mathematical Physics;Dec2013, Vol. 54 Issue 12, p123301
In two recent articles, we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry win-loss. We present in this article another generalization (always associated with a...