2-l Estimators for a discrete-valued parameter. A discrete-valued parameter with the

prior pdf

p(x) = CpJ(x - i)

i=l

is measured with the additive noise w - N(O, a2)

z=x+w

1. Find the posterior pdf of the parameter.

2. Find its MAP estimate and the associated MSE conditioned on Z.

3. Find its MMSE estimate and the associated variance.

4. Evaluate these estimates and MSE for

Case pl 0 z

A 0.5 1 1.5

B 0.5 1 3

C 0.3 1 1.5

D 0.5 0.1 1.8

5. Comment on the meaningfulness of the two estimates in the above four cases.

prior pdf

p(x) = CpJ(x - i)

i=l

is measured with the additive noise w - N(O, a2)

z=x+w

1. Find the posterior pdf of the parameter.

2. Find its MAP estimate and the associated MSE conditioned on Z.

3. Find its MMSE estimate and the associated variance.

4. Evaluate these estimates and MSE for

Case pl 0 z

A 0.5 1 1.5

B 0.5 1 3

C 0.3 1 1.5

D 0.5 0.1 1.8

5. Comment on the meaningfulness of the two estimates in the above four cases.