The model illustrated by Figure 2 generates a specific pattern of response
probabilities which can be computed from integrating the normal distribution.
So, for example, the probability of a FA is obtained as the probability
(i.e., area under the normal distribution) of finding a value larger than 2
with a normal distribution of mean 0 and variance 1 (this can be computed
with most statistical packages or from Tables such as the ones given in Abdi,
Edelman, Valentin & Dowling, 2009). This quantity is also called the probability
associated to the value 2, in our example it is equal to .0228. Along
the same lines, the probability of a Hit is obtained as the probability (i.e.,
area under the normal distribution) of finding a value larger than 2 with a
normal distribution of mean 1 (i.e., the mean of the signal) and variance 1,
this is equivalent of finding the probability (i.e., area under the normal distribution)
of finding a value larger than 2 −1 = 1 with a normal distribution
of mean 1 − 1 = 0 and variance 1. This value is equal to .1587.