Exercise: Multiple observations and unknowns
Let Θ1, Θ2, W1, and W2 be independent standard normal random variables. We obtain two observations,
Find the MAP estimate θ^=(θ^1,θ^2) of (Θ1,Θ2) if we observe that X1=1, X2=3. (You will have to solve a system of two linear equations.)
θ^1 = ___????
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