Question

2-1 Estimators for a discrete-valued parameter. A discrete-valued parameter with the prior pdf p(x)=\sum_{i-1}^{2} p_{i} \delta(x \quad \text { i) } is measured with the additive noise w ~ N(0,o²) z = x+ u: 1. Find the posterior pdf of the parameter, 2. Find its MAP estimate and the associated MSE conditioned on :. 3. Find its MMSE estimate and the associated variance. 4. Evaluate these estimates and MSE for 5. Comment on the meaningfulness of the two estimates in the above four cases.

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