Question

Please find the ML, MAE, and MAP of this question! Thank you!

(20%) Suppose that a signal s that takes on values 1 and -1 with equal probability is sent from location A. The signal received at location B is Normally distributed with parameters (s, 2). Find the best estimate of the signal sent if R, the value received at location B, is equal to r.

Answer 1

Solution : from the given data R-> Signal received at location B RaN (4,2). with Pdf fools) find ob seeved valce &. where sis parameter with the prior distribention, P (551)=P P(S= 1) = l-P The posterior distribution of the signal seat & is given by f (015-1) P (1=1) Peally) f(rls) p (271)+ f (rls-4) P (S=0) et/4 (8-12 p . é / (8-12 1/4 (r+12 pte (I-P P P+CI-D) -114 (+) P P+ (1-0) elly ( r2 cror Р P+(1-P) e lerer ::P(SW) = 1-P (Pillo) P+ (1-P) er Best estimate of sin the mean square error (HSE) Square posterior mean = 1.p (6= 1/2) + 6) p (5=t/v) P (1-P) er P+ci-per P+(1-P) é v

P-(1-P) en روح () + و وزیر امور rocofron & و در op song netore I انوار at w