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Exercise: Multiple observations and unknowns Let 1 , 2 , W 1 , and W 2 be independent standard normal random variables. We obtain two observations, X...

Exercise: Multiple observations and unknowns


Let Θ1Θ2W1, and W2 be independent standard normal random variables. We obtain two observations,

X11+W1,X212+W2.


Find the MAP estimate θ^=(θ^1,θ^2) of 12) if we observe that X1=1X2=3. (You will have to solve a system of two linear equations.)

θ^1 = ___????

θ^2 =____????

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