A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function P(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)) (1) on the domain x in (-infty,infty). While statisticians and mathematicians uniformly use the ter…
This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal…
Canadian Urological Association guideline on the care of the normal foreskin and neonatal circumcision in Canadian infants (full version)
In 2016, Karney proposed an exact sampling algorithm for the standard normal distribution. In this paper, we study the computational complexity of this algorithm under the random deviate model. Specifically, Karney’s algorithm requires the access to an infinite sequence of indepe…
A normalized form of the cumulative normal distribution function giving the probability that a variate assumes a value in the range [0,x], Phi(x)=Q(x)=1/(sqrt(2pi))int_0^xe^(-t^2/2)dt. (1) It is related to the probability integral alpha(x)=1/(sqrt(2pi))int_(-x)^xe^(-t^2/2)dt (2)…
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We have investigated with light and electron microscope immunocytochemistry the aminergic and peptidergic innervation of Onuf's nucleus in adult baboons. This nucleus, located in the ventrolateral part of the sacral spinal cord (S2 and S3), is considered to control urethral and a…
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Artificial intelligence refers to computer systems that can perform complex tasks normally done by human-reasoning, decision making, creating, etc.
The following theorem is proved. Let $X_1, X_2, \cdots, X_n$ be $n$ independently (but not necessarily identically) distributed random variables, and assume that the $n$th moment of each $X_i(i = 1, 2, \cdots, n)$ exists. The necessary and sufficient conditions for the existence…
This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive…
The distribution of a product of two normally distributed variates X and Y with zero means and variances sigma_x^2 and sigma_y^2 is given by P_(XY)(u) = int_(-infty)^inftyint_(-infty)^infty(e^(-x^2/(2sigma_x^2)))/(sigma_xsqrt(2pi))(e^(-y^2/(2sigma_y^2)))/(sigma_ysqrt(2pi))delta(x…