A choice is made between Hypotheses \(H_{0}\) and \(H_{1}\) on the basis of a single measurement \(x\). Under Hypothesis \(H_{0}, x=n\); under Hypothesis \(H_{1}, x=s+n\). Here both \(s\) and \(n\) are positive random variables with the following PDFs:

Calculate the PDFs under Hypotheses \(H_{0}\) and \(H_{1}\). Find the decision level on \(x\) to yield a given false alarm probability \(Q_{0}\), and calculate the probability \(Q_{d}\) of correctly choosing Hypothesis \(H_{1}\).

Transcribed Image Text:

Po(x) = be-bn P(x)=ce, b