For the logarithm \(g\) of the likelihood ratio defined in Eq. (9.36), \(e^{g}=\) \(\frac{p_{1}(x)}{p_{0}(x)}\). Define the moment generating function of \(g\) under Hypotheses \(H_{0}\) and \(H_{1}\) by

Show that \(f_{1}(s)=f_{0}(s+1)\). Determine \(f_{0}(s)\) for the logarithm of the likelihood ratio in Example.

Equation 9.36

Transcribed Image Text:

f(s) = {es|H;}, j=0,1.