Given a two-class problem:

Ho: p(x/H,) = e* u(x), u{x) is the step function.

H: p(x/H,) = ek-1, with p(Ho) = 3/8, and P(H1)= 5/8, and Co0C=0, Co=Cio1.

a) Find the Bayes Decision rule for deciding between the two hypotheses.

b) Calculate the average probability of error.

c)What is the probability of detection and the probability of right decision.

d )What is the threshold for the Neyman Pearson test for a false alarm rate of 0.01. e)What is the sufficient statistic for deciding between the two hypotheses given 'N independent multiple observations.