(color online) Probability computed by Eq. (6) (continuous curves) and by numerically realizations of Eq. (3) (dots) for the stochastic input I(t) with (, blue curve and dots) and without (, red curve and dots) signal. The task is to answer whether a given received input data of length T includes signal . realizations are used for averages of numerical dots. (a) . Both distributions ʼs of (red) and (blue) strongly overlap. It is difficult to make correct prediction. (b) The same as panel (a) with . With longer T the two distributions of and separated considerably. The probability to make correct conclusion becomes higher than panel (a). In both panels (a) and (b) theoretical predications of Eq. (6) and numerical results coincide with each other very well.