Let θ1 , θ2 , w1 , and w2 be independent standard normal random variables. we obtain two observations, x1=θ1+w1,x2=θ1+θ2+w2. 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.)

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