a) Consider a binary hypothesis testing problem, and denote the hypotheses as H =1 and H =1. Let a = (a 1 , a 2 , . . . , an)T be an arbitrary real n-vector and let the observation be a sample value y...

a) Consider a binary hypothesis testing problem, and denote the hypotheses as H =1 and H =1. Let a = (a₁, a₂, . . . , an)T be an arbitrary real n-vector and let the observation be a sample value y of the random vector Y = Ha + Z where Z ~ N (0, σ²In) and In is the n by n identity matrix. Assume that Z and H are independent. Find the maximum likelihood decision rule and find the probabilities of error Pr(e|H = 0) and Pr(e | H=1) in terms of the function Q(x).