2-2 ML Estimation with correlated noises. A parameter r is measured with correlated rather than independent additive Gaussian noises \tilde{z}_{k}=x \div i t_{k} \quad k-1, \ldots, n with E\mleft[u_k\mright]=0 \mleft.\hat{E\mleft\lbrack\hat{w_k}w_j\mright\rbrack}\mright?-\mleft\{\begin{array}{ll}t

& \quad k=j \\ \rho & |k-j|=1 \\ 0 & |k-j|>1\end{array}\mright. For n = 2: 1. Write the likelihood function of the parameter x. 2. Find the MLE of x. What happens if p - 1? What happens if p - -1? 3. Find the CRLB for the estimation of r. Show the effect of p > 0 versus p < 0.Explain what happens at p = -1. 4. Is the MLE efficient? Can one have perfect (zero-variance) estimate? 5. Using the above notations, write the likelihood function of x. 6. Find the MLE of x.