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Suppose we observe a sequence 1 , 2 , . . . , Y 1 ,Y 2 ,...,Y n given by = , = 1
Suppose we observe a sequence 1 , 2 , . . . , Y 1 ,Y 2 ,...,Y n given by = , = 1 , . . . , Y k =N k s k ,k=1,...,n where = ( 1 , . . . , ) N=(N 1 ,...,N n ) T is a zero-mean Gaussian random vector with covariance matrix 0 0; 1 , 2 , . . . , s 1 ,s 2 ,...,s n is a known signal sequence; and is a (real) nonrandom parameter. (a) Find the maximum-likelihood estimate of the parameter . (b) Compute the bias and variance of your estimate. (c) Compute the Cramr-Rao lower bound for unbiased estimates of and compare with your result from (b)
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