In this problem we refer to Example 8.6. Suppose the random variables (X1,Y1),(X2,Y2),...,(Xn,Yn) are all independent and that for each i we have Xi,Yi distributed as N(i,2). a) Set = 1 2 and express the likelihood function in terms of the parameters 1,...,n, and . b) Show that the log likelihood is l(1,...,n,) = 2nlog 12 + nlog n i=1 (Xi i)2 + (Yi i)2 2 . c) Calculate the MLEs for the parameters 1,...,n,.

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