How do I make a Gaussian process generate a stream of events? I would like to generate a stream of "random" gaussian events (on for event - off for no-event) that obeys a set standard deviation and mean.  what algorithm could I use?
thank you
 A: First method:
The principle
You can always transform one distribution to another through a transformation of the independent variable, so we get if $p:\mathbb{R}^N\to(\mathbb{R}^+\bigcup\{0\})^N$ is a probability density function of $N$ variables and we transform the independent variables $\mathbb{R}^N\to\mathbb{R}^N$ by some differentiable transformation $y_j(x_1,\,x_2,\,\cdots)$ then we get a new probability distribution $q(y_1,\,y_2,\,\cdots)$ defined by $q = p\, \partial\vec{x}/\partial\vec{y}$, where $\partial\vec{x}/\partial\vec{y} = (\partial\vec{y}/\partial\vec{x})^{-1}$ is the relevant Jacobian of the transformation. So you choose your transformation to transform the domains as needed, and you must choose your Jacobian to shape the transformation. Usually the input density $p$ is the uniform probability distribution generated by a random number generator.
The Practice
The Box-Muller transformation as described by:
Everett Carter, "Generating Gaussian Random Numbers"
is an excellent implementation of this principle. 
Press, W.H., B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, 1986; Numerical Recipes, The Art of Scientific Computing, Cambridge University Press, Cambridge
also describes this in full. In short, we take two independent random numbers $x_1$ and $x_2$, which are uniformly distributed in the interval $[0,\,1]$. Then we form:
$$y_1 = \sqrt{-2\,\log{x_1}}\,\cos(2\,\pi\,x_2)$$
$$y_2 = \sqrt{-2\,\log{x_1}}\,\sin(2\,\pi\,x_2)$$
and then $y_1$ and $y_2$ are Gaussian variables with unit variance and mean nought. So you would simply use, say $\sigma\,y_1+\mu$ to get a Gaussian distribution with mean $\mu$ and variance $\sigma^2$.
Second method: Use the central limit theorem. Add one hundred independent random numbers, each uniformly distributed in $[0,\,1]$. The sum will be very nearly Gaussian with a mean of $50$ and a variance of $25/3$ (equal to 100/12, since the variance of the uniform variable is $1/12$). Then scale and shift as in the first method to get your mean and variance.
