4. Consider the detection problem in the notes p.168-171 but with the threshold detector |Y | > γ =⇒ "say signal present" |Y | < γ =⇒ "say signal absent" (a) Find the probability of detection and the probability of false alarm (b) Find the probability of error. (c) Find the limiting values of the probability of error as γ → +[infinity] and γ → −[infinity].

Aprobability experiment is conducted in which the sample space of the experiment is s={7,8,9,10,11,12,13,14,15,16,17,18}, event f={7,8,9,10,11,12}, and event g={11,12,13,14}. assume that each outcome is equally likely. list the outcomes in f or g. find p(f or g) by counting the number of outcomes in f or g. determine p(f or g) using the general addition rule.