In Part I a statistical theory for the detection of a pulsed carrier in noise has been described, where specifically three types of observer are defined: (1) the Neyman‐Pearson, (2) the Ideal, and (3) the Sequential observer. In Part II specific betting curves are determined for the weak‐signal cases, and some approximate curves for strong signals are also included. The input signal‐to‐noise (power) ratio (a02)mincorresponding to the minimum detectable signal at the output (with an arbitrary probability of a correct decision) is found, as expected, to vary asn−½for weak signals and asn−1for strong, wheren=number of pulses integrated. Furthermore, comparison of observers on the basis of the minimum detectable signal reveals the Neyman‐Pearson to be better than the Ideal, by an amount 0 (0.5 db). On the basis of the assumed approximate distributionws(ns) of sample size, the Neyman‐Pearson also appears superior to the Sequential observer, but as indicated in Part I, the latter must always be as good as, if not better than the former. The discrepancy is the result of the approximate nature of the assumed distributions. A lower bound on the errors thus introduced in the calculations of the (a02)minis accordingly provided by the extent to which the Sequential appearsworsethan the Neyman‐Pearson observer for equal probabilities of type I and II errors &agr; and &bgr;. Forws(ns) =&dgr;(ns−<n>) this error is reasonably small 0 (1.5 db), but for a Gaussian distribution ofnsthe effect is 0 (3.0 db) at least. Included also are an analysis of performance and some of the factors affecting it. The paper terminates with a brief account of a statistical theory of the observation process and its relation to the various observers considered here.