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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 u…
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)))/(sigm…
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…