Computation of probabilities that involve a Gaussian process require finding the area under the tail of the Gaussian (normal) probability density function as shown in Figure F.1.
Figure F.1. Gaussian probability density function. Shaded area is Pr(x ≥ x0) for a Gaussian random variable.
Figure F.1 illustrates the probability that a Gaussian random variable x exceeds x0, Pr(x ≥ x0), which is evaluated as
The Gaussian probability density function in Equation (F.1) cannot be integrated in closed ...