2. [Matching Bernoulli parameters] Consider hypotheses Ho and Hi about a two dimensional observation vector X = (X1, X2). Under Ho, X1 and X2 are independent and identically distributed. Both have the Bernoulli distribution with p =0.5. Under H1, Xi and X2 are mutually independent, X1 has the Bernoulli distribution with mean p = 0.2, and X2 has the Bernoulli distribution with mean p = 0.8. (a) Describe the maximum likelihood rule for deciding which hypothesis is true. (b) Describe the MAP rule for deciding which hypothesis is true, assuming the prior distribution with 10 = 7 1