Appendix B. Q, erf, & erfc Functions[1]

The Q-Function

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 B-1.

Gaussian probability density function. Shaded area is Pr(x ≥ x0) for a Gaussian random variable.

Figure B-1. Gaussian probability density function. Shaded area is Pr(xx0) for a Gaussian random variable.

Figure B-1 illustrates the probability that a Gaussian random variable x exceeds x0, Pr(xx0), which is evaluated as

Equation B.1. 

The Gaussian probability density function in (B.1) cannot be integrated in closed ...

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