Assume that we have measured a single observation of a random variableX. The model forXis

X=(1B)G1+BG2

whereBhas the following distribution:

P[B=0]=P[B=1]=12

G1is(0,2)andG2is(,2). Assume thatand2are known and thatB,G1,andG2are independent.

(a)Find the posterior distribution ofB.

(b)Find the MMSE (minimum mean square error estimator) estimator ofB. Plot the estimator as a function ofX.

(c)Find the MAP (maximum a posteriori estimation) estimator ofB. Plot the estimator as a function ofX.