Consider the following binary hypothesis testing problem. Under Ho, the random variable X has the pdf...

 

Transcribed Image Text:

Consider the following binary hypothesis testing problem. Under Ho, the random variable X has the pdf fo, while under H, the random variable X has the pdf fi, where fo(u) = {} \u [}]}] 0 else and u fi(u) = = u [0,2] +1 u(2,4]. 0 else Assume that 40 = 1. (a) Find the ML rule. (b) Find Pfalse alarm: Pmiss, and pe for the ML rule. (c) Find the MAP rule. (d) Find Pfalse alarm: Pmiss, and pe for the MAP rule. Consider the following binary hypothesis testing problem. Under Ho, the random variable X has the pdf fo, while under H, the random variable X has the pdf fi, where fo(u) = {} \u [}]}] 0 else and u fi(u) = = u [0,2] +1 u(2,4]. 0 else Assume that 40 = 1. (a) Find the ML rule. (b) Find Pfalse alarm: Pmiss, and pe for the ML rule. (c) Find the MAP rule. (d) Find Pfalse alarm: Pmiss, and pe for the MAP rule.