1) You collect 100 measurements x[0],...,x[99], which are realizations of i.i.d, random variables Xo, X1, ..., X99 following the Gaussian distribution with variance 2 but unknown mean u; i.e., X; -N(1,2). Assume you need to build detector to decide between: HO: H=1 H1: = 1.5 a) What is the form of the Bayes Risk detector that minimizes the expected cost assuming that the a-priori information is P[HO]=0.75 and Coo = -1 Coi = 10,000 C10 = 300 Cu=-5 where Cij is the cost of deciding for Hi when Hj is true. b) What is the expected cost of the detector of item a) ? 1) You collect 100 measurements x[0],...,x[99], which are realizations of i.i.d, random variables Xo, X1, ..., X99 following the Gaussian distribution with variance 2 but unknown mean u; i.e., X; -N(1,2). Assume you need to build detector to decide between: HO: H=1 H1: = 1.5 a) What is the form of the Bayes Risk detector that minimizes the expected cost assuming that the a-priori information is P[HO]=0.75 and Coo = -1 Coi = 10,000 C10 = 300 Cu=-5 where Cij is the cost of deciding for Hi when Hj is true. b) What is the expected cost of the detector of item a)