Unformatted text preview: 1 was sent. b) Is this rule the MAP rule for any prior probabilities on the message M ? If so specify the probability p = P ( M = 0) for which this is the MAP rule. If not, explain why not. 4) Consider a binary hypothesis testing problem where the observation is R and its conditional distribution is given by Given H : p R | H ( r ) ∼ N (1 , 4) Given H 1 : p R | H 1 ( r ) ∼ N (-1 , 1) a) Show that the optimal decision rule is equivalent to comparing a function of the form ar 2 + br with a threshold. b) Find a and b when p = P ( H ) = 1 / 3 ....
View Full Document
- Fall '11
- Probability theory, hypothesis testing problem, binary hypothesis testing